Tele = tele
puzik = belly!
telepuzik = telebelly!

Telcom is a russian game sever ran by the Belarus Institute of Higher Education
Its a very small one though, that acts as a portal to play the games you mention in your post Quake, Counter Strike etc, the page you posted is the forum that all the "clans" meet up in to discuss tactics, cheats, teams etc.

It has a mail server though and a mailing list on the home page so maybe that could be what the Unsubscribe page was for??

As you pointed out Negative the emails where sent out from Universities and this is a university web site running what is basically a public access mail server!?!?