As an only child, I've never had any issue with playing board games by myself. Or card games. Outdoor games were harder; Red Rover is tough when you've got no one to call over.
All said because I always loved board games, and Christmas was prime time for getting them. Toys were the main goal at Christmas. Other people got clothes, and were excited about them, but since my mother made all my clothes, and made them year-round, they weren't going to be special in December. Also, my father was a GIVER. And a SPOILER. You get the picture.
In my experience, therefore, Christmas is the time for toys and records and cool stuff that you didn't/weren't going to get during the year. "Serious" presents must be specifically requested.
When my children got old enough to ask for things outside of the toy aisle, it was sort of sad for me. Hannah and I, though, truth be told, still love going to Toys 'R' Us and just walking around. The toy department at Target, too. And I sometimes still happen across things there that I tuck away as "fun" Christmas gifts, "surprises" that weren't on either child's list.
Christmas ought to be fun, is what I'm saying, I guess. And the 26th is always in play as just a continuation of the 25th. You don't go anywhere, and you've got all kinds of new stuff to enjoy.