Board Game Arena

How do I launch an official appeal to a time violation due to a game bug?

There's no official way. I guess you contact support? But assuming you're talking about a time penalty (which it would seem you are as you don't have any exit penalties), time penalties mean almost nothing - they don't affect your karma, they don't put any limits on your play and people can only see them if they specifically go to your profile. And I suspect most people wouldn't even glance twice at 3 in 182 recent games (especially if you're acknowledging the other two time penalties as justified - the difference between 2-3 in 182 games would mean nothing to pretty much anyone you play), assuming they actually checked your profile. Frankly, I'd argue it's not worth your time to contest it. Just move on.