The AI, at the start of each game, picks one of a handful of "Grand Strategies", generally one per victory condition. This choice then weights the Flavor values that the AI uses to decide what buildings or units to build at any given moment. Also, the AI has an inherent diplomatic penalty against any other players or AIs following the same path to victory.
So, if you turn off everything other than a Domination win, then the AI just won't pick the "culture", "science", or "diplomacy" grand strategies. Every civ will take the conquest strategy, which'll weight things towards military buildings and units over infrastructure, and will change how many units get built in a typical game. Also, with every player on the same grand strategy, it'll probably make the AIs less friendly with each other (thanks to that penalty I mentioned above). So yes, this'd probably translate into a more aggressive game, although not the sort of all-out warfare you might expect; the difference might not be noticeable for some AIs. Flavor shifts are not THAT severe; a civ biased towards gaining culture (like France) will still do so, and civs biased towards city-state alliances (Siam or Greece) will still do that. It's just that they won't bias quite as severely as they would if you'd left those victories on. And no one will try to build a spaceship, because turning off the victory condition automatically disables the Projects involved.
Dedrytus, while you're correct that the AI doesn't account for most of the optional rules or other setup options, this is one of the few cases where the AI DOES recognize a change, albeit in a very crude and random way.