OK, so I'm totally promoting something my kid loves, but I think there might be other geeky game-type kids on here who might love it too, so I will. The more kids, the more fun for all.
They run everything through a secret FB group and through a club on chess.com
A chess coach in Arizona started an online club for homeschool kids and has been running a "summer camp" that my son's been part of for the past couple months, with live online tournaments, video lessons, a FB group with discussion and puzzles, and lots of opportunity for kids to challenge the other kids. The kids range from beginner to pretty good and I think most are 6-13 yrs old, with a lot in the 8-10 yr old range.
Video chess instruction and puzzles are pretty easy to find online -- kids to play games against are not so easy to find, so having the club has been great. There's going to be a fall semester too (we'll do it again for sure), and I think it's cheaper if you sign up in the next couple weeks.