Disclaimer: I am not a structural engineer, nor do I play one on TV
That said, the International Building Code specifies a uniformly distributed live load design weight of 40 pounds per square foot (psf) for residential construction. I don't know the species of the wood your beams are made up of, and it does make a difference, but even Eastern Spruce (as opposed to Yellow Pine or Douglas Fir) can carry over 40 psf live load @ 15' span. Basically, your room exceeds code (as Woody76 points out, probably closer to 50 psf).
Of course, the weight isn't evenly distributed across the room. As stangbat mentions and you point out, the pins will be lined up along the walls, the best place to be for carrying weight, as much of the load will be transferred directly to the support (basement) walls below them. That leaves primarily the people which on a weight basis is well below the design loads. Without going into all the possible exceptions like concentrated load or, also as stangbat points out, a dynamic load of dancing/jumping, you will be fine. You would most likely notice any significant floor deflecting well before failure anyway. If you want, you could just see if a ball rolls to the center on those hardwood floors, or run a string along the joists below attached at the ends and mark the spot in the middle where the string is. You will see any deflection in both cases after you load the pins/under full party load.
Have a fun Tourney!