In that video he should have said "using a Tig torch instead of a resistance weld". He said "using a Tig torch as a resistance spot welder.
He did say the tungsten is recessed into his cup, correct there is an arc. The amps and time are dependent on metal thickness and should be tested beforehand. I have done that in the past and it does work, no ring for the cup and no copper but yes clamped tight. Nothing wrong with the ring and the pad on the vise grip, probably makes it easier to position and clamp in one shot.