Yeah, because getting up quickly from the one without arms is probably less of a prop hazard. Makes a lot of sense given the kind of personnel movement that takes place on the bridge.
What I could never for the life of me figure out is why they didn't secure the chairs down with steel dowels into the floor. Any moving vessel should have chairs that are locked down. It's only sensible, no matter if you're on land, air, sea, or space.
Of course, the real reason was probably one of cost and time savings.