Presumably there is a channel on the other side to move the clip when carrying on the other side. He threaded his belt through the channel.
Reminds me of an armored car guard I would periodically see at the Federal Reserve Bank (near where I picked up the commuter van). He had some form of revolver in one of those Uncle Mikes hunting holsters. He would undo the "retention" strap while walking to the building. The strap was so frayed it looked like a small rodent was hanging from his holster.