If it's a party composed of workers and it advocates specifically on behalf of the interests of the members, then yes I would call it a union. If party membership is open to anyone and labor issues are only some of the planks in its platform, then no I would not call it a union.

Honestly I think this is just continuing a very uninteresting semantics discussion - now we have to decide what "labor party" means. The point here is that you seem to have a different definition of "union" than the average person, which is fine, you should just be aware of that and watch out for misunderstandings when you're discussing with someone so you aren't talking past each other.