I'm really glad you enjoyed the game.
I admit, that the role of the tree for gameplay is very abstract and indirect, but the goal of the game effectively is to protect the tree as your character needs it for recharging stamina.
here is a more detailed explaination of the mechanic if you want to read it:
Although it is not explained in text, the more you kill, the more the red vines choke the tree, and as this happens, the white orbs that come from the tree which recharge your shield at the start of each round will slowly be currupted and turn red (when this happens, they will no longer recharge your shield), so by protecting the characters "oath", you protect the tree and last longer, which is the goal of the game.
sorry for such a long reply.