If this is an actual game session, I kinda doubt you’ll get to ad ANY supplemental lighting except for *maybe* an on-camera light. If it’s a staged even specifically for shooting footage, then you can do anything you want.
Laser tag games don’t “require” darkness-the beams are Infra-Red, and for insurance purposes, the game areas usually have adequate and artistically arranged lighting so people running around don’t get hurt. Though I can imagine a few areas might have spookier lighting in them, that’s likely not the case overall.
My gut says to hang a variable-powered LED panel on the camera and just do what you can, if it’s a real game. If the gaming area is kind of open, and there’s a balcony for spectators, maybe an LED follow-spot, aimed at your “hero” from a distance, manually tracked by a helper?
(Was doing this back in the 80’s in Arlington Heights, IL when it was called “Photon”. You wouldn’t believe how bulky the gear and helmets were)