That answers only half the question as any previously installed AV could leave remnants behind and these could clash and have a great impact.
The windows firewall shouldn't be involved as it doesn't monitor outbound activity.
Unfortunately I know nothing about gametap or how it works, so it is difficult to even imagine how avast could be involved.
If you only play the game on-line, it may be how the game is delivered, if streamed through the http port 80 it would go through the web shield proxy and it must conform to the HTTP protocol. If it doesn't then it could fail in the web shield filtering.
Try this first, Terminate the Web Shield and see if that allows you to play the game on-line (assuming you are playing it on-line).