I love how the motion is shown in the melee attack and throwing animations! The art is very simple and crude but at the same time looks good. Just a couple of minor issues, I think - the sand (background) is too saturated, taking some attention away from the monsters, and the health is white text on a bright-orange heart which is hard to read.
The gameplay is quite fun. As you've mentioned yourself, though, the jumping is useless, and I've noticed that my health doesn't really matter. You could do away with the jumping control and the health (taking damage is still to be avoided because it slows you down) and the gameplay would still be the same. Or, of course, you can add reasons for them to exist, such as more damage being dealt, enemies that attack and shoot, and some things that roll on the floor towards you and force you to jump?
Edit: An idea to make the jump useful - you can make the jump faster than running and make hitting enemies while falling down deal more damage. Unfortunately it's not my idea - it's how it already is in Minecraft - so I don't know if it's okay to implement it.