I dig this game a lot! I really suck at 2D platformers so take my feedback with a big grain of salt because these are not my forte:
- I wish the jumping was a bit snappier. The weightlessness of it made it harder at times than I think it needed to be.
- I LOVE the rope mechanic. I'm a sucker for games where you can swing like Indiana Jones. That to me was just so fun. I'd go so far as to say that should be the main conceit of the game.
- On that note, I'd even say that the whole combat/shooting system could be removed, which would sync up better with the narrative imo: if he's trying to not be an awful person, instead of blasting his way through time cops, having him maneuver and navigate around them would make more sense.
- The humor is awesome. I like how the watch breaks the 4th wall.
So yeah, I think this has all the makings of a really cool game. Great job!! :)