In this post I'm going to attempt to come up with a comprehensive taxonomy of game genres. I claim that games can (and should) be classified according to at least the following traits: competitive or casual, replayable or scarce, turn-based or flowing, and perhaps others. I'll discuss the pros and cons of each trait in each category.

Replayable Games

These games are played in "matches" or "rounds" that don't build on each other and that you can sit down and play one of whenever you want. They have the obvious draw that, assuming they're designed well, they never get old. You can play these games for a lifetime without ever feeling like you've "finished" them.

Replayable games are usually played against other people, but computer opponents can be created. They can support both competition and cooperation, and have great potential for customizability. Most replayable games have tunable parameters that give the players the freedom to play their own type of match. Dominion, for example, depends heavily on what cards are available, which can be manually picked out by the players or randomly generated.

Scarce Games

These games depend on content (such as levels or a story) that must be hand-crafted and which can only really be experienced once. That seems like a huge downside. And it is. But the persistent nature of these games allows levels to build on each other in a way that isn't possible in a replayable game, which can provide a feeling of "progress" that can't exist in those games. These games can also make up for their scarcity by making each level uniquely satisfying in a way that the non-scarce matches of a replayable game can never be. I'll go over two ways of doing this.

Story Games

This type of game seeks to act as both a work of fiction and a game at once, taking advantage of the special properties of interactive media to enhance the story. A game that does this incredibly well is Doki Doki Literature Club (I can't say any more without spoiling it).

Story games have huge potential for emotional impact. If the story is done well, they can leave a mark on the player's soul that leaves them thinking about it for years after they've finished it, or even for the rest of their life. It can be even more powerful than a book or movie ever could, because the interactivity of the video game format helps achieve a level of immersion that's simply not possible in a non-interactive medium.

Puzzle Games

In a well-designed puzzle game each level feels like solving a new problem and learning something you couldn't learn from any other level. It's a lesson that "sticks with you", not as much as a good story, but more than a match of a replayable game.

Another big point for puzzle games is the concept of a level editor. It's not hard to make one and it gives it more or less the replayability of a replayable game (albeit it's not as efficient because each level still has to be hand-crafted). Even if the developers don't release it for community use, the nature of puzzle games allows them to easily crank out new levels once they've built a solid foundation of rules, whereas story games don't become easily extensible like this.

In addition, puzzle games have an advantage in that you can never really lose. Puzzle games have no need to ever send the player back a few minutes like story games sometimes do. They aren't as tilting or salt-inducing as competitive games can be.

As another downside, puzzle games are usually inherently single-player. The mechanics are just incompatible with idea of multiple players. And while you can of course give advice, that's not as fun as actually being in the game with someone.

I should also mention that it's possible to mix the two methods above. Portal is an example (albeit the "story" could never stand on its own).

Competitive Games

This type of game gets its primary appeal from challenge fun. It's something you can improve at and compete with others to be the best. Or, in a scarce game format, you can raise the difficulty for a second playthrough to see just how far your skills can go.

A good competitive game can be enjoyed even while you're not actually playing matches of it. You can study it, analyze your mistakes, discuss strategies with other players (even if it's an action game there's usually some element that can discussed like this), and, at least in a replayable competitive game, train apprentices. Replayable competitive games are also often great for spectating, which allows you to enjoy the game without the stress or commitment of actually playing.

The only bad thing about replayable competitive games is that you can't really dabble in them. This is because if you know you don't plan on getting "into" it, you can't appreciate the depth in the way that you have to to fulfill the point of such a game. Making matters worse, since you never "finish" a replayable game, you can only experience so many of them. Back in my gaming days being into just Prismata and Go at the same time took up almost all of my gaming time. I don't think I could have gotten into a third competitive game without dropping one of them. And they don't leave a mark on your soul like story games do (see above), so if you do drop one you don't really take anything away from it. All the enjoyment of playing it is in the past.

And as for competitive story games, the competitive mechanics tend to bottleneck the story, creating a conflict between the game and the narrative. The more times you die at a plot-heavy boss fight the more you're reminded that the story isn't real and there aren't any consequences for failure. While it's incredibly satisfying to finally beat a boss that killed you a dozen times, it's likely to hurt the immersion of the story.

There's a flip-side though. If done well, making the player struggle for the victory can help them appreciate the heroes' physical struggle more.

Casual Games

This type of game focuses on accessibility and appealing to a wide audience. They should be played with large groups. A good example of a replayable game that fills this role and does it well is Codenames. For a scarce example, I'd mention Lego Star Wars for a good one, perhaps Elder Scrolls for a bad one.

The draw of this role over competitive is that you don't need to be "into" it to play and enjoy it. You can introduce someone to this game and have an enjoyable match with them right from the start, even if you're an experienced player. The main ways they achieve this include: a ruleset simple enough to be learned while playing, team play or even fully cooperative play (such as Codenames: Duet), no player elimination, making it hard to tell who's winning until the end, and (if not fully cooperative) some sort of way to give a weaker player a chance against a stronger player. This last one can be achieved in many ways. Prismata, although it is a competitive game, shows a great way to do this that doesn't involve randomness: performance variance. Each game of Prismata has a different set of units available for purchase and therefore a different optimal strategy, and since your "skill" is essentially how well you play in each set averaged out, odds are not bad in any single match that a weaker player will pick a better strategy than a stronger player.

The downside - and it's a huge one - is that they can't really be taken seriously. You can't get "into" a casual game, because it doesn't have the depth of a competitive game.

Where story games are concerned, a casual paradigm removes any conflict between the game and the story. On the other hand, it also kind of kills the possiblity of using gameplay challenge to help the player appreciate the story as well as that of using difficulty settings to multiply the game's replayability.

Turn-based Games

Turn-based games have a few obvious advantages. They can be interrupted when they need to be and aren't stressful - except in cases of competitive replayable games where you need turn timers, but in those cases time management becomes an interesting part of the game's skill set. On the other hand, time spent waiting for your turn can be different degrees of boring, and gets worse the more players you have.

Turn-based games against AI, though... that's a nice exploit. Having a computer opponent more or less eliminates the waiting time.

The best turn-based games mitigate the bore of waiting by giving players something to do or think about on their opponent's turn. Go is a really good example. In the intensity of a battle for the life of a group, you try to "read" (play out possible variations in your mind to find the best move) during the opponent's turn as much as possible, and it's not any harder or less effective than reading during your own turn (except that you risk it being for naught if your opponent makes a move you didn't plan for). The effect is that it doesn't really feel like waiting.

Prismata is similar, but not as good. In the first few turns of a Prismata match you need to look at the available units and come up with a strategy. It's the most important phase of the match, so players who are good at time management will spend a lot of time on it. But, as with Go, you can think on your opponent's turn, and so this creates a really interesting metagame where you might pass your turn even though you're not done thinking - and only part of your time will store - because your big decision comes next turn and you want your opponent to pay the time cost for your deliberation. If the opponent takes a while and does something you didn't expect, then you just profited big because now you also don't have to waste time planning for moves they didn't end up making. But if the opponent immediately does exactly what you expected and passes, you might find yourself profitless and forced to make a decision with less time than you wanted. The reason I said "but not as good" is because in Prismata this usually only extends for the first few turns, since once you get into the meat of the game where math becomes involved it gets very hard and inefficient to read ahead.

Flowing Games

Flowing or "real-time" games have an enormous advantage in the elimination of waiting time. They can also be more exhilarating. But they lose the time management skill, introduce potential problems with lag or network latency, not to mention how it might look like the game is bullshitting you (such as fighting game situations where you could swear you were blocking but somehow the enemy hit you anyway) and the player doesn't have time to look at it and see how it's fair, and in a strategy game it can be frustrating to have the better strategy but lose anyway because you couldn't click fast enough or something.