Honestly, I love it when the sexy-stuff is part of game mechanics in some form or another, but sadly, that sort of thing is rare. At least when compared with all the games out there where the sex is barely part of the story, much less the gameplay. Or the games where sex is sort of "just there", where you can remove all the smut altogether and the gameplay and narrative aren't really affected...
As for mechanics that I've enjoyed, in no particular order...
1. Sex for Breeding Mechanics - You've already mentioned Monster Black Market, but there's also Goblin's Burrow that's in this category. Then there's Naedoko Demon's Ground where the protagonist needs to have sex, be impregnated and spawn monsters that she commands in battle. There's some other games that hit this niche, though I can't remember any really notable ones off the top of my head.
This is obviously more of a thing for pregnancy fetishists, all things considered, but it's still a tangible mechanic that affects gameplay, or around which you can build an entire gameplay loop.
2. Brothel and/or Sex-Slave Mechanics - Anyone still remember Slave Maker, where you had to train random girls into slaves, which includes sex skills? There was a variant of that specifically focused around managing a brothel. Since then, there have been other games that have similar ideas in some form or another, but there's not that many of them because the management aspect they tend to get into end up being pretty niche. I suppose those "train this one single girl" games sort of count too, but barely.
AV shooting could be considered a subset of this. There's some games that basically focus specifically on making AVs and selling them for money. There's that one Ressentiment game that I played a while back, and there's also that game from Team Krama, though I haven't played the latter yet.
3. Sex helps with empowerment Mechanics - One of the most commonly known examples for this are Acerola's Cum Collecting games, where cum you collect literally translates directly into character power in various ways. Whether it's Melissa where leveling and upgrading outfits is done specifically just with cum, or Colette where cum is part of the Alchemy system too, etc... the fact remains that sex isn't just a reward for the player, but something the characters in the game world need to think about and interact with. Ruins of Luxoria also falls into this to an extent, as you get skill points as Saria and the MC have sex (with the amount varying on the circumstances) and in general, Mishiji's games tend to have some sort of empowerment mechanic tied to sex.
There's other ways to use this too, from getting buffs, using it to make money or some other form of currency, part of rituals for games with magic... the possibilities reach as far as one's imagination and setting allows.
4. Battle-fuck games - Karryn's Prison is likely the most well known game in this area, where sex is part of combat in all of its forms and basically everything is some form of potential sex battle, including the various jobs around the prison. It's the only game off the top of my head that puts such a high level of emphasis on sex during fights to the point where you can do fights with just sex. There's some other games out there that at least have more to sex during battle than just random in-battle rape... but they're rare and aren't anywhere near as complex. Sadly, this is a mechanic that is overall under-utilized... though to be fair, making it good is quite complicated for a lot of reasons. I suppose Last Evil sort of counts too in this category? Not entirely sure...
This is all just off the top of my head, and there's sub-variations of various kinds that I'm probably forgetting at the moment. A lot of what's doable also depends a lot on what kind of fetishes and niches you want to hit. Hell, even the tone of the game's story can influence what kind of mechanics you have, or at least, their exact form.
