This looks fun! The chase rules and the unarmed combat rules both land well, and the PDF and encounters have strong 8-bit vibes. Overall, I think this is solid work, so what follows are just nitpicks.
It’s a little unclear whether a character can jump-kick, combo, and throw an object all in the same turn. I assume the answer is no, but it might be worth stating explicitly. I also don’t think we ever get stats for the three artifacts, so GMs will have to invent those themselves.
The “directions” the kobolds give are a bit vague as well. If we had explicit hints, clever players might be able to locate the lair earlier than intended. Finally, I don’t think the PDF ever explicitly names its inspirations. River City Ransom for sure, and likely a Mario game as well. But i'm unsure on #3
Great work! You should be proud of this.