I'm looking for a way for family to stay connected/kill time across the miles. Any suggestions for games that can be played on iOS, Android and maybe PC?

Most users won't be interested in an "arcade" style game. Something more like a board game would be better. There could be 5-10 people from age 30 to 80 interested in participating.

I know I'm kind of asking a lot. A possible option might be if there's a way to set up a game room where different pairs or smaller groups can choose what games to play together.

Everyone in the group has a facebook account, but few are frequent users of it currently.

My friends use to pay scrabble together.
They seemed to really have fun.
I can't spell so I didn't get into it.

Most of the classic family boardgames and card games have mobile apps now. Monopoly, Battleship, Scrabble, Uno, etc.

If you want something similar but a bit deeper, many of the bigger name "Euro"-style board games have mobile apps too, such as Settlers of Catan, Carcassone, Ticket to Ride, etc.