This sounds very fun. I used to do something similar with a character in tabletop superhero games, running a "lottery" power and rolling random ones to manifest at given times. I have been sticking to one on ones lately but this sounds like a good time in a group. If you are looking for input, I would say that points-based killing would have to be thought over a lot before committing to it. Unless players can run more than one character, or there are "NPCs" able to killed off, there might not be many opportunities to earn points that way. But in general the idea for an economy isn't a bad one.

If I may ask as well, what kind of aesthetic are you going for? Battle Royale and Hunger Games both have characters that skew younger. Were you looking for like an anime-style high school killing game, or a grittier more realistic adult cast?