It is a 577 T-Rex. It is owned by a Middle Eastern gentleman named Saeed. He owns and manages
www.Accuratereloading.com. They have a whole collection of those videos on that sight. That is actually Saeed's indoor range where the video is filmed.
If you post a certain number of posts (I think 200) he sends you a free DVD of your choice. He's an upstanding fellow who runs a great sight. I need to start posting there again.
It's funnier watching the middle eastern guys shoot it.
Oh yeah, it's for hunting elephants, a hobby that Saeed participates in regularly.
edited to add: It's probably not considered a "destructive device" in UAE or Africa, the two locations you are most likely to find this particular weapon.
also edited to add: Check out the results of one of his safaris:
forums.accuratereloading.com/groupee/forums/a/tpc/f/1821043/m/352106011