Thanks a bunch for reaching out!
I'd say a common high level way of categorizing physical games would be:
- Tabletop board games
- Tabletop role playing games
- card games
My major interest is RPGs and as people mentioned being able to tag with by systems such a Fate, PbtA, FitD, Gumshoe etc. would be wonderful.
Of course, many designers create their own system, so have the option of creating some sort of imprint tab for one's own system would be great, and really helpful for the consumer to find all the rule books, rule expansions, settings, adventures, zines, maps, pawns and other material that are related. Even for indie publishers, it's not unheard of to have more than one core game, so being able to sort by line could really help people find this.
It would be useful to have some way of categorizing the type of RPG: class-based, skill based, narrative, OSR, experimental
Universal would be a helpful tag--people do write content that is not tied to a specific system.
In addition to the genres people have mentioned, I'd add pulp and mystery as being