I don't know if I'd characterise Dwarf Fortress as a game where "the AI tries as hard as it can to beat me". As far as I understand, the AI for mobs (and dwarves) in the game is pretty rudimentary, not much more than pathfinding -- it's just that the rules of the game (= physics of the simulation) are very unforgiving.

It looks to me to be similar to taking a small open boat across the Atlantic -- can be done, but any mistake or just bad luck can have dire consequences. And yet this is not the case when something tries to beat you, there is no malicious agent involved.

What other games you play that you think offer further examples?