I most enjoy interactive and confrontational games. I find most joy in tabletop experiences that engage me with other players, rather than just engaging in an optimization race against them or collaborating over a puzzle. When judging a game, I think about all the below features that can make games fun. No game hits on all these points, but I generally find that the ones that hit on a lot of them become favorites of mine.
1. Is the decision density high? Is the ratio of interesting/trivial decisions high? Decision making is the heart of what makes non-athletic games fun.
2. Is there a collective play space? Do player controlled pieces exist in the same place, or does everyone have their own play area?
3. Can I interact with other players in a meaningful way, or is it just a race? Is the interaction arbitrarily mean? Is willful direct conflict common? Is it clear how my actions will affect other players?
4. Am I interested in what other players are doing? Engagement with other players is an important aspect of tabletop gaming to me. Can a player do well by ignoring other players at low levels of play?
5. Is there significant downtime? Not playing is significantly less enjoyable than playing. Short turns, simultaneous actions and interrupt mechanics help alleviate this. Two player games have an innate advantage here.
6. Is it easy to tell the state of the game "at a glance"? Can you quickly and comprehensively ascertain the status of your opponent's game components? This is important for enabling engagement and good decision making. Many games have components that make this difficult (e.g., separate player boards and cards with small text)
7. Does the game overstay it's welcome? Shorter is generally better than longer. Sometimes longer is worth the added depth. Some of my favorite gaming experiences are long. This is more of a positive "get it to the table" fitness characteristic than anything else.
8. Does the game state change so significantly between turns that it is difficult to plan? This is significantly more problematic if downtime is long.
9. Is the game accessible? Is the learning curve too steep for what it offers? Simplicity is generally better than complexity. Complexity can be rewarding if your players are willing to learn the game well.
10. Does it feel thematic? Does the theme complement the mechanics? Or is it just an abstract game with window dressing? Thematic is generally better than abstract. Sometimes abstract is the right choice.
11. Does the game have appealing aesthetic? Beautiful art. Table presence. Both at once is sublime.
12. Are the mechanics fragile? Does game play degenerate or break when players play in an unusual or sub-optimal way? It is a common problem in highly interactive games for an unskilled player to unknowingly act as a kingmaker.
13. Is there clarity about how the game will end, and who will win? Clear ending conditions are good. Perfect information about the score can detrimental to morale and anticlimactic, especially if victory is secured too long before the game end. Lack of clarity about the relative scoring position of players can be anticlimactic, especially if adding up the score after the endgame is a length process. Tight, clear and decisive endgames are generally better.
14. Is play overly deterministic? Overly perfect information can lead to clearly optimal paths of play, which can cause AP and boringness. Randomness is not the only way to smash determinism.