No, they don't. Many people will say that a game would be better with some "competition" where you actually have to work or you might lose your love interest to some NTR antagonist or whatever. That would be fine if that's what the game was going for, it all depends on the game. But seeing as I love playing games with story and character growth, that's very surface level to me. You don't necessarily need an antagonist, you just need a compelling conflict and this may or may not include an antagonist.
I'm sort of desensitized to antagonists in adult games because most of them are sex hungry, brain dead, kong dick idiots who only serve to sate the NTR fetish. Most antagonists in adult games are *not* written well whatsoever. They're only written with enough sense and more than enough dick and sex drive to service the already nonsensical plot and I think I'm referencing about 80% of adult game antagonists with that statement.
But games like Broken Dreamers and BADik have an interesting conflict that their antagonists flourish in and that's just naming those 2, there are more definitely. The conflict is the environment around them and they feel powerful as a result.
e.g. Meredith of Broken Dreamers makes you feel paranoid. She has eyes everywhere. The city feels like her domain and you're just trying to navigate through it and break out. Not only that, but that's only enhanced by the inner conflict of the people who associate with her like Victoria, who you have the option of breaking down the walls she keeps up to do her job efficiently.
Quinn of BADik is a powerhouse in the school caste system and school is plagued by peer pressure and bullying. Stuff that the MC can tolerate, but someone like Maya is having trouble with. Accompanied by the issues she has with her father's lack of acceptance.
These characters are antagonists but at the same time, they feel like pieces of something that's bigger than them. It doesn't start and end with Meredith and it sure as hell doesn't start and end with Quinn. The city was a mess before Meredith and it will still need a whole lot of cleaning up after her. And the school system will never change. Quinn is just a product of a broken system in place. The system and whatever obstacles in her life bred what she became and now she reigns supreme over it (for now).