It's definitely possible to classify most TTRPGs within existing storytelling genres. Is there any kind of standard list of genres that appeals?
A lot of TTRPGs are based on specific systems - e.g. Wretched & Alone SRD, Carta SRD, Peregrine SRD, Princess with a Cursed SRD - and tagging this systemic origins can be helpful for finding specific kinds of games.
When we were trying to do this, we also tried to tag games by number of players. We never finished structuring things or making a form for adding and editing games, though.
URLs change, but it still might be good to include them.
Special equipment - conspiracy boards, tumbling block towers, Tarot cards, etc. - were another thing we were tagging.
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Some disorganized thoughts to mine for ideas: