Is there more to the game than just Start battle > click the level up button as many times as you can > click the recruit button as many times as you can > repeat? Do I have to get to a higher level to do more stuff or am I just missing the point here? 

im with you on this one i couldnt find the difference between start and auto battle either 

Yes, there are more things you can do. You can move and order your units to maximize the battle potential and the profit. You can also decide on the composition of your army. Later you also unlock prestige upgrades.

But in general this is a semi-idle incremental game, so the key concept is just "the numbers going up".

This was also a very early demo (prototype) and soon we'll be adding more content.