HVAC geek here,
I recognize the parent poster's humor, but take exception with the conclusion that more air conditioning capacity would be required.
The cooling system for a gymnaisum should (1) provide enough fresh air for the room's expected occupancy, (2) maintain a comfortable temperature between the lowest seating and the highest seating, and (3) remove water vapor provided by sweaty athletes and heavy-breathing spectators.
A dehumidifying air handler should take care of (1) and (3), while destratification fans would blend the air for consistent feel over the height range described in (2).
During a LAN party, there should be fewer occupants in the space than during, for example, a basketball game.
These occupants would be seated and thus lower to the ground than running and jumping athletes or spectators in bleachers.
Overhead lighting levels could be reduced to limit glare on monitors, probably down to the density required by code for emergency egress.
From 9pm to 3am, the building envelope would not be subjected to the heat load of solar radiation.
If destratification fans were turned off and CO2/H2O sensors were used to control the outside air intake and dehumidification stages of the air handler, respectively, the cost of cooling overnight LAN parties may be less than the cost of cooling the space during its designed use.
Just my $0.02