While i never got around to playing it, I've heard good things about Myhouse.wad (Doom 2 mod), it's story is more so something you figure out from the environment (no narrator). But it's directly inspired by House of Leaves and it has multiple endings.

Mainly recommending it because you mentioned "user involvement" and you can't get much more involved than a video game. If you do play it, i recommend reading the original forum post and the google drive which features stuff that expands on the story and gives hints on what you're supposed to do in the mod.

Here's the link to it. https://www.doomworld.com/forum/topic/134292-myhousewad/