I find putting games down pretty easy whether I like them or not.
I rarely "beat" a game. But, then, a lot of the games I play aren't really the type you can beat, anyway.
I was going to write somewhat the same thing. Plenty of games don't have a clear end goal (multiplayer and puzzle games, mostly), and even the games that do feature an end state often have so much sidequests and extra objectives that it's debatable when you truly beat them. Heck...rocksmith 2014 has somewhat of a campaign, but when do you really "beat" a game like that? Playing 'through the fire and flames' without fault? Or 'just' better than the actual band?
And there's somewhat of the opposite as well: virtual board games, for example, are played in relatively short sessions. You can quickly burn through many of them if you consider "winning" as "beating the game" (especially if you pick the ones where the AI isn't up to snuff).
Ahem...so just to say: I can name plenty of games. I'd even nominate my own favorite game, UT2004. It had a campaign, but since it's a multiplayer shooter I literally refused to finish the campaign for years.
...nonetheless, I think the game I'm currently playing qualifies even more on the criteria: Santorini.
Santorini is a board game app that is very simple in nature. You and your opponents each take turns moving one of your two pawns in any direction (at most up one floor, and not into someone else) and then building a floor next to that pawn. The winner is the first who manages to climb to the third floor (or manages to completely trap the opponent).
It has 5 AI skill levels. The usual game convention would have the lowest skill play as a toddler. In this game, the AI is one I'd still occasionally lose to. Itching out a win over an AI one or two levels higher is a (serious) achievement. I've yet to even manage to get close to a win on anything higher.
But it's worse than "just" the game having AI that makes alphago blush. you see, the above game description is the base version. However, you usually each pick a starting power that remains with you for the entire game. There are a few dozen types of powers...and every single one changes the basic game in an almost completely completely different way. So I'm not just NOT winning...I'm in the position that even if I ever manage to scrape out a win against the best AI (probably after hell froze over)...then I can still look forward to restart attempting to learn to play against an entire different playing field.
The game itself is great, though. Just...I don't think I'll live long enough to ever come close to what you can consider "beating" the game.
