Really cool concept, something i´ve not seen before, but some feedback:
1. Remove the jump function, as the game is interesting enough without.
2. Add some animation or something for the player, just make it more alive and not immediately go to the place.
3. Make the perspective more like in subway surfer, or make a grid were you can see where you are.
4. Make it so there are no restrictions when it comes to how far the player is from the other player.
5. Make the graphics less "unity". They don´t look bad, but a different background color and a nicer color scheme would make things much better.
6. Use a different font than arial.
I hope the feedback helped you, would be nice if you could check out my submission too. :)