Looking at this game you played this week, it is not surprising you are still being surprised by some of the nuances of the rules of chess.
I suggest you read some of the many fine articles available here and watch some of the online video lessons about how to open a chess game.
You need to learn the concepts of developing and coordinating your pieces and pawns to favorable places to maximize their power, making your king safe and so on. Your concept of trying to win pieces is not wrong, but it is certainly not something you can pursue while ignoring other key strategic areas of the game.
My strategy is to deploy my peices towards the center quickly, create a battery or two, that's opening, and than the midgame is destroy every and all peices I can, and than once that is achived, go for the checkmate. I think I could do better if I balanced destroying peices and getting my enemy checkmate.
However, I played a game against a rookie, and I was winning by a score of 12 (piece value wise) but I didn't get him into checkmate, as I got him cornered where he couldn't make any legal moves, so therefore a draw. I was proud and confident, but now I feel like a poor player. I know some will say this is butthurt, but can someone give me more confidence/words of wisdom.