Because "bramka" means literally: "a little gate", so you may translate this word as "a goal", "a tagret" etc. "Siatka" means literally: "a net", but a player cannot run to a net, it sounds weird in Polish. You can say: "Piłka wpadła do siatki" - "A ball fell into a net", but it sounds weird in English, on the other hand. I think this translation above is correct.
'The player is running to goal' is more typically spoken if that person is involved in the game.