What specific games were your main influences in designing YHTWTG?
So many games. I suppose VVVVVV is the obvious one, even though I didn't ape its primary mechanic. But it was very much the reason I chose to implement named flip screen rooms, though of course that mechanic dates back to classic games like Jet Set Willy.
Bubble Ghost was a big influence on the visuals and tone. It had a sort of creepy, unsettling vibe, not only because you were exploring a haunted house with some grim imagery, but because there was a sense that you didn't belong in that space. Its hazards operate autonomously regardless of your presence, and everything can kill you.
Indiana Jones and the Last Crusade: The Action Game was another big one for me. I used to play the DOS version of that game on a four-color CGA screen all the time. The first level involved exploring a cave, which is probably subconsciously why I set so much of YHtWtG in subterranean locales.
The "magic word" / "magic symbol" puzzle originated as a riff on the in-game copy protection mechanisms you'd see in classic PC games, where you'd have to look up a word in the manual or use some in-world secret code reader to find a solution and advance. This puzzle (if you can call it that) evolved a bit due to practical restrictions, and I had to change it once more when I brought the game to Steam, but that's where it started, anyway.
The feel of the wall slide / wall jump mechanic was inspired by Mega Man X and Super Meat Boy, as opposed to something like Super Metroid with its obtuse triangle jump. I also made some tweaks to help make the platforming a little more forgiving, things like allowing the player to jump a split second after walking off a platform or immediately jumping again if the button were pressed a split second before landing on the ground, after reading an interview with Team Meat in which they were describing similar improvements to handling in SMB.
I wasn't consciously setting out to make a Metroidvania, but the structured nature of exploration limited by abilities found in the world did evolve from those sorts of games, to include Zelda titles.
I wasn't consciously riffing on anything specific in the bullet hell rooms, but I am a fan of bullet hell shooters. Ikaruga first got me into the genre, and at some point I started collecting Cave shooters and Mushihimesama Futari quickly became my favorite.