This game takes me back to playing games on the GBA or even occasionally on the NES, very reminiscent of the past. The beauty of making games inspired by older games is that they are really simple to make with modern day engines. Your choice to do something like that, intentional or otherwise, definitely worked for you as this game is incredibly polished and everything plays really well. The graphics are really good, almost professional if this was a game on the GBA/NES. Audio add to the level of polish overall creating an enticing experience. Gameplay is fairly simple, but works in its favour, with two options leading to a 'Rock-Paper-Scissors'-esque scenario where you can outsmart your opponent. Despite the simple controls, complex decisions can be made. You even added a jump forward and back motion with double tap! This, with perhaps some tweaks here and there could be placed on a marketplace.
I feel like an ability to choose an arena from the menu would be a nice feature, as it took a couple of retries to get to see all of your arenas. The main improvement that I think should be made is the hitboxes as avoiding damage can be a little difficult at times, and a slightly smaller hitbox would help compliment the "Simple but Complex" system that you have designed. Finally, consider your controller bindings for local play. Whilst you can play both systems with 1 or 2 hands, it does feel like player 1 would have a smaller advantage since movement would typically be controlled by the left hand. Are there other keys that you could have used to mitigate this problem?
That being said, most of my critique can be considered nitpicks as this game is well polished and the issues encountered would have little effect on general play between two people. This is definitely a strong submission that you should all be quite proud of. Well done!