Dwarf Fortress is a great example, of the "The AI only has to win once" variety.
It largely determines which games I play, and for those I want to play which don't adhere to my preferred rules, I modify until they do. (It's much less satisfying than when the game is designed for it, granted.)
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?
"In one sense, because of the game’s procedural design, the entire universe exists at the moment of its creation. In another sense, because the game only renders a player’s immediate surroundings, nothing exists unless there is a human there to witness it."
"Through the use of procedural generation, No Man’s Sky ensures that each planet will be a surprise, even to the programmers. Every creature, AI-guided alien spacecraft, or landscape is a pseudo-random product of the computer program itself. The universe is essentially as unknown to the people who made it as it is to the people who play in it—and ultimately, it is destined to remain that way."
More at:
http://www.theatlantic.com/technology/archive/2016/02/artificial-universe-no-mans-sky/463308/