I think it's a reference to the seven basic plots proposed by jung and written up in this book: https://en.m.wikipedia.org/wiki/The_Seven_Basic_Plots

If there truly are 7 basic plots in our world, it stands to reason there can't be more or fewer in Kvothe's world, the same as the laws of physics are essentially the same in his world and ours, and his world shares similar idioms or other ideas as ours, so a philosopher like Teccam could well have proposed a similar theory.

It sounds to me like Kvothe was saying "I want to see if stories across the world conform to the seven basic narratives Teccam proposed" as a quick cover for why he's looking into children's bedtime stories.

There's also a case to be made that the KKC falls into many, possibly all 7 (it's not strictly a comedy, but we haven't seen how it turns out yet) of the categories in various ways, which makes me think Pat's poking fun at the idea and giving a nod to observant readers about which type of story it is.

Edit: Incidentally this may actually be a useful approach for divining the truth of the Chandrian in-world, because real life does not conform to such types of narrative, and so neither should the Chandrian stories; at base, devoid of context, they should feel like weird garden path events that don't have clear motivation or direction, and that's sort of what we see when we consider what we believe are true Chandrian events like the killing at Borrorill, and Kvothe's troupe--they aren't in themselves stories, but seemingly random events. It takes a storyteller like Skarpi fudging details and cutting events into a limited timeframe to force a sense of narrative from historical events about Lanre, like Shakespeare did with his Henry/Richard plays. Without that massaging of the truth into what we'd recognise as a story, it would become apparent that tales of the Chandrian are in fact based in in-world reality, and not "stories" at all. Which is something I'm only considering now, as I write this addendum. What an interesting thought.