I'm not sure how to make the area within the trigger PvP only.
There are things you can do to deter players watching the fight from being able to interfere or fight amongst themselves:
applying 100% spell failure
unsummoning everything
add perma true seeing for easy viewing of the fight
setting all players friendly to one another
have the area heartbeat check and cancel any actions from any players not flagged as being in the arena
etc
These could be done OnAreaEnter and removed when leaving or when entering the PvP section of the arena. I've not done this myself and do not know if that would adequately cover everything.