I know this is an old post, but I thought I'd reply anyways!
That's actually my video haha, guess I'm not surprised someone on here found it.
People are right, separate species shouldn't be housed together that is just asking for trouble. However, when it comes to play times together, I think it really depends on the individual animals. Some GPs are more aggressive than others, same goes for Hedgies and everything else. Mine both happen to be pretty laid back. Any time a critter is with another one they should be CLOSELY supervised, especially if they're being introduced for the first time.
Another point is, take care in choosing what critters you let meet. For instance, I would NEVER have my gerbil and degus together, not for a minute. Nor would I put either of those with the Gp. They're far too spastic for him.
As far as "socializing" the Gp and hedgie, they really don't care about each other, so they really are only ever in the play ground together when I'm cleaning cages, other than that there's really no reason to have them play "togther".