So, back to the OP, here’s some more suggestions unusual ttrpgs:
Puppetland: you play as sentient puppets, fighting against the tyranny of Punch, the Maker-Killer, and his army of Boys, sewn from the dead flesh of the Maker of All Puppets.
Weave: uses fairly traditional dice mechanics, but most of the game, including characters and “campaign playbooks”, are on your mobile device. To create a character, you are dealt a hand of tarot-like cards, which you scan into your mobile device; each card gives you a set of options for character abilities and flaws. It lets you quickly build a complex character with an interesting backstory, but you can’t pre-design a character. Also, hefty up front cost ($60+ for the game for not a lot of physical content). Also, while the mobile device usage makes it highly portable, since you have to have everyone always on their device and online simultaneously, it is a real power drain. And not playable if you don’t have a good internet connection.
FATE: you probably already know about this system, as it’s fairly well known. The major published books (Spirit of the Century, Dresden Files, Atomic Robo) are all really well done, but fairly traditional games, albeit much more narrative than games like D&D. Their Worlds of Adventure line of pay-what-you-want PDFs, though, can get fairly wonky.
DramaSystem: if you think rules for social interactions and roleplaying get in the way of actually roleplaying, avoid at all costs. If you want ANY combat rules or crunch, avoid. Otherwise, it’s a really interesting, fairly minimalist approach to roleplaying dramatic conflicts.
GUMSHOE: another one that you probably already now about, but just in case…GUMSHOE is a fairly traditional, mid-weight rpg system, with a bunch of different settings, from the Lovecraftian horror of Trail of Cthulhu to the over the top, slightly campy wild time travel adventure of TimeWatch. It’s set apart by three things. One is that it was designed from the ground up for investigative adventures. You can definitely run more traditional action adventures, but the emphasis is really on investigating, gathering clues, and solving mysteries. The second thing that sets it apart is the publisher, Pelgrane Press. A sort of “mid-major” company, it produces an almost ridiculously high quality of graphic and physical design for their books, and features a stable of top-notch writers and designers (including my two favorites, Kenneth Hite and Robin Laws). The third is a sort of house approach to adventure and world design, which gives you hooks and seeds and evocative quotes, and usually at least two versions of any given NPC or location to help customize it to your own home campaign.