Battlenet Thinks Game Is Running Mac

For the past few days I've been learning how networking works on a Mac, but I came across a problem at a school I work at with kids and their online gaming.
The school uses iMacs and a Mac server, though kids on campus use both Macs (various kinds and different OSs) and PCs (again different OSs). Surfing the net for information is slowing to a crawl because a lot of the kids play online games and not just from battle.net but others as well.
The issue is that we don't know which games are being played so knowing the exact port for that game/company is hard to figure out. I did a few searches online and got port numbers for battle.net and few others, but seeing how I'm sure I don't have them all I need to find a simple 'one click' method where one port or one block can shutdown all online gaming no matter the company.
The library computers as well as the head computer the teacher uses all run 10.4.x. I need to figure out how to block a PC port on a Mac server, as well as a Mac on a Mac server but my guess is that blocking a Mac on Mac is the same as PC on PC (or I could be wrong on that too).
Any help will be much appreciated.
Machines

Battlenet Thinks Game Is Running Mac On Mac

Varies, Mac OS X (10.4), OS Range 10.4.x

Download manager. For users who commonly encounter intermittent connectivity issues or download failure, a download manager may help. Download managers are a third-party application that can monitor, and if needed, resume a download from where it stopped previously.

Battlenet Thinks Game Is Running Machines

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