Nah look in full screen, pause it at 0:15. That's a gun. The other thing that you actually see him pick up is a cell phone. He never actually captured him picking up the gun. Dude who made the video just said in the captions that he saw dude in the gray sweater pick it up. In the video, you only actually see him pick up the cell phone, which is closer than the gun.
But yeah, it doesn't mean dude had a gun, cuz it was awfully far away from his body. Plus that might not even be the same .45 they recovered later. They are being overly secretive which is making the gun story look shady. If they were straight up about it, they could just dust the gun for fingerprints and see if it was his. and they would tell us whether it's the same in the video.