I`m wondering if you are suposed to just destroy your enemies to win or race... or both

From what I read, the goal is to win the race. Destroying your opponents will be sort of a means to that ends. I haven't read a lot about the game so I may be way off here, but that's the way I interpret the game.

I hope there will be some kind of last man standing match stuff

I got this game today, it's both. You are trying to end in 1st place, but you are also trying to destroy your opponents and the environment if you want. There is a Lap Knockout mode too, alot better than any Burnout game's Lap knockout! Btw, you can blow up anything you want!!