Everyone has their own way, but honestly, he fumbles a lot. He should slow down a little. I'm very coordinated, but I don't try to move that quickly with gunsmithing activities. Slow is smooth, smooth is fast. But then, maybe your filming made him nervous.
I strip receivers completely, put them in the vise with aluminum blocks. I made my barrel wrench, which clamps down on interchangeable alumimum blocks for different barrel profiles and diameters.
I try not to judge, but IMO, a 3 jaw chuck doesn't have much application in gunsmithing unless it's an adjus-tru, which that one isn't. For profiling, I turn between centers with a dog, or using a 4 jaw & live center. For threading, 4 jaw with spiders, or cat's head, because no barrel I've ever encountered has a bore perfectly concentric to outside profile. I suppose it's OK for receiver truing, although I'd still use a 4 jaw independent and indicate the thing.
I use two different lathes for smithing. Most of my barrel threading is done on my Hardinge HCT with an auto threader. The auto threader is electro-pneumatic, and if set up properly, gives perfect threads. I can thread right to a shoulder at 1,000+ RPM, giving superior finish. I usually re-crown with a beveled counterbore, unless someone specifies otherwise. This is the Hardinge:
And this is how the auto threader works (not my video):
My other primary machine is a 1920s Rahn-Larmon 17 x 60 engine lathe that I reconditioned and upgraded:
Believe it or not, it's a very precise machine now. Just yesterday I had to repair a totally boogered 1911 that someone had already tried to install oversize grip bushings in and screwed the pooch. On this machine, I made a .252-60 internal thread, 5/16-40 external thread bushing from 316 stainless and saved the frame. Could have been welded I suppose, but that would have wrecked the cerakote and presented other problems.
And my giant cat's head, a 3.5" ID x 5.5" OD 6061 aluminum tube with eight 3/4-16 set screw I made brass tips for to center the work piece within. I can put an entire barreled action in this thing, including semi autos and lever guns:
That's a 9" diameter bearing it rides in. That steady rest I made from raw stock as well, is 2.5" thick 7075 aluminum. For one, I couldn't find one at any price for this machine. Two, they likely wouldn't have had such a large capacity and three, I wanted a really trick set up with my fingers that allowed large contact area with bearings to avoid gouging the part. These are the fingers, which each have six ball bearings that self-align to the work piece as the adjustment screw is tightened due to my multi-piece design:
I also made a rotary threading attachment for the big machine so that I can get right up to shoulders on that one manually rotating the chuck with no worries of crashing, or missing a mark trying to thread away. It's pretty slick, I used an ER-20 collet holder through a boring bar holder I pocketed for bearings, then made a 6.6:1 gearbox to reduce the up to 30,000 RPM 40x92mm brushless motor down to a more usable range:
Just messing around with a dovetail cutter on C360 brass:
It also works much better than a static cutter for interrupted cuts, or threading really thin tubing.