First (and most obviously), make sure that your guitar and strap are firmly connected, whether that means eyebolts and chain or whatever. Make sure you're wearing your guitar low, at least right before the swing. Know where your bandmates are, and KNOW how much space you need.
Second, he went the wrong direction with the swing. The best way I know to do this is to put your fretting hand at the top of the headstock and push down and across your body, leading with the body of the guitar heading around your back. The bass player in this video does one that way at 3:15, but it happens so quickly you only get a glimpse:
I've done it quite a bit, and If you get it right, it looks cool to the chicks, but you need to practice it quite a bit to get down the swing. Also, it is easier to do forward swings as opposed to from behind. Don't however, practice this with your main guitar, grab a cheap piece of crap for practice time..............The REAL Rocker.