Hey Majord, I just saw this post when I was looking into setting up a Streets of Rage Brawler and saw that you still have not gotten the issue resolved after posting other places. What exactly is the issue you are having?
I took a super quick look at it before work and notice that the collision detection was on the main body of the sprite, instead of on the hands. I am also new to Construct 2 but I think, if you set an image point on the animation and pin a collision box to it, you should be able to apply damage to the enemy. Right now if you run into him the you die.
Also the movement on street of rage is an 8 directional movement. A tutorial made on faking the jump with an animation it pretty good.
8 Direction Jump Tutorial
You might want to check out the platformer section in the How Do I Frequently asked questions by Kyatric. The one about the Grabbing the edges of a platform/wall might help too.
I won't have time to dig deeper into your file for a few days. But if your question is about the collision detection it should be an easy fix.