That all sounds pretty good. I think the more, the better, as long as you think it's above level. This all sounds above level because in my (limited) experience of ordinary 5-6 year olds, 1) I don't think most of them would know much at all about the solar system-- maybe just beginning to recite the planets; 2) I don't think most of them could answer any/many questions about any/many countries, let alone locate them on the atlas; and 3) especially if the game you describe was invented by your son, it shows he's inventive on a higher than normal level,
plus able to spell, something that kids often don't do well at all until age 6-7 or later (I guess this would depend on the types of words the video shows him spelling, i.e. the vocab level).
I wouldn't worry about embarrassing him. Everything I've read about your son points to him being a special little boy. The Davidson folks must review scads of applications, with kids that are all over the map in their different skill levels. Just go for it.
Does he like building things? Any sort of work output might be a good target, as long as he's done it all himself. Does he use computers much? What other sorts of games does he play?
Also... you might not like this, but I really think that asking him to expound on all his musical knowledge, loathsome as some of it might be to you

, might really do the trick. If he has great pitch and can really remember whole songs, you might want to stopper up your ears and have him beatbox a bit too. It can't hurt! One of the general criteria they seem to look for is how deeply a child dives into a subject, any subject. And while I know you have some fears over that particular expression of interest, it might really help your application.