does the salad dressing that comes with the salad at the japanese restaurant (the ginger one) have gluten in it?

Yes. It usually contains soy sauce and sometimes miso, which is questionable.

I would not take a chance. As missy'smom said, they usually contain soy sauce or miso. If not then ponzu which is just as bad.
I usually ask for lemon and shichimi which is a red pepper spice.