Does a court determine whether a party is a sublicensee under a license containing 
an arbitration clause through a motion to compel or is that done by the arbitrator?

Dear Streetlight, 

I am sorry that your question is about to expier and hasn't been
answered yet. However, this could be becayse you haven't written about
the jurisdiction (laws change from country to country; sometimes also
inside a country there are different jurisdictions, e.g. - between
states in the U.S); and haven't written any further details about the
case.

Maybe, if you posted it again with such details, one of us will be able to help you.