I'm not Chuck, or Bruce, or the Reverend Jessie Jackson, but I did stay at a Holiday Inn last night.
Dry welding is referring to forge welding without a flux. Just to clarify a forge weld is a cohesive bond of the layers of steel across the entire surface area with NO filler material (the bond between layers in damascus) achieved by applying force to the layers while at the proper temperature.
Typically, most smiths add a flux (anhydrous borax is very common) to a billet prior to forge welding the layers together. The flux keeps the inner surfaces of the billet free from oxidizing while reaching the proper temp.
With dry welding, you weld the seams of the joining layers with a mechanical welding process. Wire-feed welding them is getting more common... Chuck did his with a TIG welder. Welding the outer edges of the layers in this way negates the need for flux to keep oxidation from occurring in between the layers.
A flux free weld is very clean and rarely results in any voids or inclusions.
edited to add: I see Bruce beat me to it. Bruce said the same thing I did but in a less confusing way. Way to make me look bad Bump!!! Couldn't leave it at beating me by one day on the membership? Now this?!?!?! roflmao
