Curiosity got the best of me, so I pulled a stack of cards out of the Genus set and started sifting through the cards, wondering how old they were, asking my brother some of the questions that he may know along the way. I managed to narrow the possible release dates between 1976 (thanks to a question about the 1976 Olympics) and 1990 (thanks to a question about East Germany) but didn't have time to go through the entire stack.
Enter Wikipedia! Wikipedia says Trivial Pursuit was released in 1982, and the Young Players edition was released two years later. Yes, this is intellectual cheating, considering I probably could have figured it out by going through the whole stack, but as the game wasn't mine to start with, it's the best I can do.
My new hobby: figuring out the ages of things by context.
This still doesn't answer why my uncle had a set in the first place. I'd say for his kids, but they were really young back then, and they're not the type to like trivia games, either.