pretty good crease in the frame in the first video. guy has all the tools but bending metal does not appear to be his field of expertise. putting heat when he used the hammer was completely unneeded, I'd use the wood block and the hammer to fix that dent. it would be difficult if not impossible to get that crease out 100% without the stud welder/slide hammer, but he could have got it closer if he tried.
the stud welder guy is not very good with metal, but he is a collision guy, not a craftsman. he does show how they work though.
as for using a stud welder on a vintage bike frame those studs stick pretty good, if you hold the trigger too long you will burn a hole even in thicker vintage automotive sheet metal, with the thicker steel of a bike frame you could get a stud to stick good enough to use the slide hammer to pull it out. I could fix that dent in the frame with no filler at all and it would be easier on a thick vintage bike frame than the butted tubing of the one he is fixing.