Sleep in a gym hall? I don't remember sleeping much at lan partys. Besides, there were more kids than computers, if you fell asleep you lost your seat.
I guess what gp is saying is that not everyone that attends the LAN party is able to sling along their computer to the venue so there are more people than machines and of course limited seating for folks without a machine.
BTW, the gp said you might lose your seat and not that your seat gets stolen since there aren’t enough seats to go round, there will always be someone who has been standing for while ready to take you seat.
Some people played until total exhaustion, so around 3AM you started to see people fall asleep while playing. That's the moment the hopefull looker in the next seat would gently grab they keyboard and mouse and 'borrow' the sleeper's PC and finally join the game.
Good times. Don't ask about the smell of the room after a 2 day fragfest.