Army of Tentacles: (Not) A Cthulhu Dating Sim is a Steam visual novel/RPG loosely based on H.P. Lovecraft's The Shadow Over Innsmouth. In it, you recruit Eldritch horrors and fight conversation-based battles. When it first came out, it went to great lengths to proclaim that it wasn't a Cthulhu dating sim. Now it has DLC that... turns it into a Cthulhu dating sim. It's all very tongue-in-cheek, but it's good for a handful of laughs. You attend a university full of Lovecraftian strangeness. Eventually, you get to date Cthulhu. Somewhere in there, things get a smidge apocalyptic:
Starting off where the base game leaves off, you must help Riley finish his romance novel. Little does he know that what starts a silly little romp into waifus and tentacles being everywhere will quickly escalate into a reality-ending crisis. What H.P. Lovecraft dating simulator would be complete without having to save the entire universe from eldritch and unfathomable horrors from beyond time itself?
Yep, sounds about right. Army of Tentacles is brief and sometimes too fourth-wall-breaking for its own good, but it's also cheap and clever. If you want to date Cthulhu, it's probably your best option, in part because I'm pretty sure it's your only option.