May be a sorted "Favourite games" list definition for each player would be useful. Then to the filters could be added: show favourite games only, also sort by favourite games could be added
(for example if one makes a list: 1.backgammon 2.nackgammon 3.hyper backgammon, then if (s)he has some running games of these they would appear on the top in this defined order). And in combo boxes then could also appear "Go to the next game of favourite type" or something similar.

Also an alternative solution instead of filters for games could be a compressed list with + to unpack and - to pack like in discussion boards browser and I bet such one is planned to group messages in discussion boards into conversation threads by topic, too.
Don't worry I will stop here for now, I don't want to fill whole discussion board with my ideas