Leela Chess PUCT Mechanism How do we know w_i which is not possible to calculate using the tree search only?

From the lc0 slide, w_i is equal to summation of subtree of V ? How is this equivalent to winning ?
As you noted, w_i is not calculated by the search tree. It is simply the number of wins out of the total simulations performed at that node (if this is the method used to score the node). This scoring mechanism is also known as playout.