This is a misunderstanding. A situation where "either process A or process B gets a resource first" is not a race condition. A situation where both of them get it at the same time is.
Even if there is parallelism and multi-core, it is still a question of ordering, and from there we can use language like who gets there "first" [indeed "race" suggests this]. Or, did this read of a machine word see somebody else's write, etc.
