having pretty much just a story with no interactions is a subgenre typically referred to as "kinetic" visual novels, so you might have some success looking under that label

Someone mentioned The House in Fata Morgana, and it's an absolute masterpiece (although I haven't gotten around to playing the sort-of prequel game, A Requiem for Innocence, yet). It's technically a romance, but there's no dating, it's just one story. There are a few choices, but they're mostly pretty obvious, and they don't really lead to branching plotlines, they just end the game prematurely.

It's amazing, I was bawling my eyes out pretty much every chapter. It does have some pretty heavy stuff though. It also fits the horror aspect, there's plenty of spooky stuff (you're in a mansion that's supposedly haunted by a witch after all). I guess overall it'd fit under gothic romance (with gothic horror elements)? I'm not particulary clear on the various literary subgenres, but "intense emotions, both positive and negative, the emotions are at an all-time high" definitely applies here.

The art is really interesting too. It's a very unique artsyle, and while the characters themselves are drawn with a lot of details, the backgrounds have this more smudged watercolor vibe, which seems weird at first, but works out pretty well. It really nails the atmosphere, the soundtrack is pretty cool as well.

VA-11 Hall-A: Cyberpunk Bartender Action is a bit more "gamey", since you have to mix drinks, but it's not really challenging - you have recipes telling you what to do and no time limit. It's mostly linear, the only impact you have is by serving certain specific drinks at certain times to unlock extra dialogue and story bits. But conversations are typically linear, you don't make dialogue choices. It doesn't have dating (although romance comes up), it's just people hanging out at the bar, very chill and comfy. Also absolutely amazing soundtrack, and pretty great art.