"some games like this? Any genre" = AVN (Adult Visual Novel)?
not all in the list below have the open world aspect, but if they dont, they excel in other ways :
Once in a Lifetime as mentioned,
im losing faith in Deviant Anomalies not because it has gone wrong already, i just get the feeling its gonna go downhill, but i might be very wrong if the author sticks to his gameplan, it is open world,
Man of the House is kinda responsible for this whole 'open world AVN' becoming popular - highly recommended fully completed game,
Leap of Faith has great renders and an almost epic feeling story (its got the whole fuck-a-superstar-celebrity thing going on, plus a very intense 'rescue-girl'),
Mythic Manor is developing well, by the same author as Man of the House but very different by having more Japanese tropes, open world,
Treasure of Nadia long game, great storytelling, excellent vanilla sexiness, (and its prequel Lust Epidemic is almost as good - while being more aimed at the cougar trope) open world, these games have more of a "real game, with AVN aspects" kinda feel to them, it feels like yr playing the game, rather than just reading a story, meaning no disrespect to any standard storytelling AVN game, just saying these games have both,
RIPPLES (quickly becoming the AVN with the best/most unique story with great renders (my use of all-caps is deliberate, the game earned all-caps),
Harem Hotel, a small open world, confined to the hotel, but dont let that put you off, lots happens there, it has a long story so far,
i'll mention Dark Magic for its really long playtime, renders are out of date, and it gets a little iffy with a child at one point - just breastfeeding, nothing sexual or otherwise illegal, but there is a nudity mod floating around - and i know child nudity alone doesnt make it illegal or wrong (its normal in some cultures) but treat it with caution as this is an otherwise sexual game and i felt it was wrong to include it in the game, and there definitely shouldnt have been a nudity mod made for it, i'll definitely warn you away from the childs' nudity mod, but game is otherwise pretty good, yr the only man on earth, and all the chicks appreciate that), open world, dont expect meaningful choices, but its a good story, and again, its looooong,
Tale From The Unending Void, solid sci-fi story, banging green chicks AND your both sisters and cousin and it looks like yr aunt will be getting some in future updates too,
THE HEADMASTER (a masterpiece for making the absurd fairly believable, goddamn that game makes me laugh and fap at the same time) total spankathon, adorable abuse of position, and all round good times, open world
Bad Memories gets a n honourable mention (for its render quality, and the story is becoming quite good),
Apartment 96 (not 69) is off to a good start as an open world AVN,
Life Changing Choices aint too bad although the renders are getting dated even with its new 'remastering',
i havent mentioned Being a Dik yet, as you've prolly heard of it (and if you havent, you dont deserve to), has open world events,
Halfway House has a unique'ish story which is well-told (and even with its very small cast, the characters are quality in all ways),
i'll highly recommend Love of Magic for its epic storyline, where you get to wield god-like powers to save the world with your harem of 'witches', dont be scared off by the poker aspect if yr not into poker, its got very little to do with the game, and you will never actually play a game of poker in the entire game, its just an analogy for the magic casting, great epic-scale story, open world AVN, i think it is the scale of the story that makes it so great, open world,
Fetish Locator is a solid game with a wide variety of fetishes and ample warnings/options to skip what you dont like,
... and reserving the best for last, for its emotional rollercoaster so compelling that even a sadistic cunt like me had some feels, a game that you can get really immersed in the excellent storytelling, loveable characters, and relax knowing it is a fully completed game from the author of Being a Dik, everyone should play Acting Lessons as their first AVN, i cant recommend that one enough, but be prepared, it WILL rip your heart out and shove it up your arse, tenderly.
Screenshot from The Headmaster:
Summertime Saga, which admittedly should have been on that list, it is a little more cartoonish in art-style, but it is open world, pregnancy and birth and re-impregnation, and pretty funny from what i remember. The children 'disappear' from the game once grown up thou
theres also another game ill mention, but it has zero story, because it is not a visual novel in any way shape or form, it is in fact a medieval, survival, 1st-person, city builder - Medieval Dynasty - and it get a mention because it does indeed have pregnancy - you get to build a village, recruit girls to work in your village (well, you can recruit the guys too, but who does that??) you can actually marry one of the NPCs that inhabit your village, get them pregnant (no sex scenes) and the child then develops into an adult and when your character dies of old age or otherwise, you take over as the 'offspring' to continue the game, assuming they have survived, thus propagating your dynasty. no kids = game over.
(actually you should recruit guys also, cos they will reproduce and grow your village also)
last update got me a lil worried is all, and its not even anything i can put my finger on, as i said, i like the gameplan, the vision of a detective game with actual investigating! idk, maybe im worried it will devolve into a pixel hunt? or maybe it was that walk back to the city, my feet still hurt :p or maybe it was just that i was waiting for a new case to work on (don't worry, i understand that a case takes a LOT of time to develop compared to a storyline).
in any case, i am certainly not saying "dont play it", i encourage everyone to go find dildo boy in your game .... and walk past him repeatedly ;) the game has a truly masterful vision, and has lived up to it so far