The author came back with instructions to fix this - they will also work on the app so it wont allow the user to do this in the future
0) Quit BG Online
1) Locate the Terminal app and open it. You can open it e.g. via Spotlight or Launchpad
2) Paste the following line into the Terminal window and hit return:
defaults read com.multimedia-go.BackgammonOnline bannedUsers
3) This should show you the list of banned players. If you are the only one on the list or you don't care about resetting the list you can just enter the following line and hit return:
defaults delete com.multimedia-go.BackgammonOnline bannedUsers
If you do want to retain the other players in the list, enter the following line into the Terminal and hit return:
defaults write com.multimedia-go.BackgammonOnline bannedUsers -array player1, player2, …
where player1, player2, … are the names of the players you want to be blocked.
4) Quit Terminal.
5) Open BG Online. The list should be updated and your user name visible again.