I loved the look and movement, and the story was hilarious. Unfortunately to begin with, I was one of the ones who for which the game didnt seem to work properly (Couldn't take any damage or deal any damage) and I know that this isn't an issue for you, so I decided to do a bit of bug testing. I noticed that actually, I could get both taking damage and dealing damage to work properly by simply hitting myself with the grenade launcher explosion once - For whatever reason, hitting yourself with the grenade launcher makes something magically tick in the game's logic that makes it so you take damage and the enemies take damage again. Of course, once I had the grenade launcher, I was in the final level, and there was no way for me to go back to a previous level, but hopefully this information helps - I would start by looking at how exactly the grenade launcher's self-explosion damage works in comparison to other weapons and why the grenade launcher in particular may cause this sudden "tick" that causes the game's damage systems to start working properly again. I guess that worse comes to worse, you could brute-force a bugfix by hitting the player with a grenade launcher explosion at the very beginning :) Let me know once you think you have solved the issue, and I'll happily give it a bug-test again to see if it runs as it should on my computer!
In any case, I saw how the game was supposed to work from your presentation and I found it just generally very impressive! The only recommendation I have is that given the excellent movement, it would have been great to see a little more verticality in the levels (there was a bit of this in level 2 and the final level). All in all, very well done!