Ludo (which I guess is it's own game, but I've always thought of as Parchesi) is fun if long-ish. "Sweetland" is fun for the whole family. One button control. Pure chance. The youngest gets to be "competitive" and the oldest gets wrapped up in the drama of the spins of the dial and jumps ahead/penalties. And for us (the parents) it's just a nice way to engage with the kids knowing everyone has the same chance. It's totally not a game of skill, but that can be nice since you don't have to feel the need to "handicap".
That's really it that I've found for board games, but it seems like a great platform for it.
I mentioned the two-player mode of Crossy Road. My son (7yo) also enjoys "Goat". Which is like a modern Qbert? My daughter (3yo) digs the Thomas The Train "Express" game.
Then there's "Starwalk Kids" and "Solar Walk". Those manage to hold their interest a bit as well while I talk about the solar system with them.
It really does seem like a great platform for family time. The biggest issue is handing the very sensitive controller around and inadvertent rolls of dice or spins of a wheel.
I'm fairly excited to see how this develops... Hopefully the awful app discoverability doesn't crush otherwise worthy apps we'd be interested in.
I haven't followed the AppleTV at all but this seems interesting... do you have time to go into more detail regarding the game(s) you have found best?