This really reminds me of the older SMT games, both setting-wise with all the demons & gameplay-wise. I also really appreciated your sense of humor. And I love the look of a lot of the enemy portraits.
Combat's tough-as-ball's but once you know how it's done it seems fair for the most part, and it's great that you can just restart a battle if you lose. And thinking about it, having your ass handed to you is probably the best way to really teach a player to run away from fights if they're too hard. I might've just been unlucky, but it took me a lot of tries to capture my first demon for a supposed 50% chance.
However I will beg you for a map--not necessarily a map that shows the entire floor right from the start, but at least one that gets filled out as you progress through the dungeon. Just something to make navigating a bit easier. I could take a screenshot of the dungeon layout when I'm getting teleported in but I'd rather not.
And a small nitpick: the camera just seems to be angled down a bit too much.
Here's a video of my playthrough. I hope it helps!