There really isn't enough information in your post to diagnose what might be the source of the memory consumption, but I would hazard a guess that when you play the online game in question, this causes the IRCbot to dynamically load one of it's dependancies that consumes some extra memory? For example, IO::Socket::SSL is loaded dynamically when a SSL connecting is required. Could this be the source of the memeory consumption?

That said, 2 and a bit megs is little enough these days that it hardly seems worth worrying about. If the increase occurred every time you made a new connection it would be worrying, but as a one time hit it seems more than acceptable for the functionality you are getting as a result.