Ok. I found your problem but I won’t be able to fix it for you. It’s in your animation.
You want to move your character through your animation. (this is called root motion) However, in your the actual animation asset the root bone doesn’t move:
This is why in your game when you make the move your capsule stays in place:
After you fix your animation (make the root to move with the character), re-import and enable RootMotion it in the animation asset, it should work.
Let me know if it does 
P.S:
The other way to do this is to keep the animation “in place” and move your character procedurally, similar to how the default jump works. However, this move is much more complex and you’ll have to know exactly how you want the character to behave in the air.
Also here is another person with exactly the same problem: