Organizing by platform and then just shoving the multi-platforms into their own kinda-somewhat-not really organized section is the best I can think of. If anyone else has a better method, I'm all ears.
Beat em up I feel can go into action, but if enough people whine about it, I'll make it it's own genre. Defense added. Flight if enough people whine about it. Mini-game added. Rail shooter if enough people whine about it. Run and gun could be platformer, TPS, action, but again, whining. Roguelikes for RPG, unless whining.