It's a standard unfinished basement with perimeter drain + sump pump. I'd say that's not a wet location but that's my opinion.
I made the run the same way the other supplied GFCI circuit is run - NM cable stapled to the board nailed on the concrete wall up to the joist cavity then run within the joist cavity, stapled every 4 feet where run parallel, not stapled where running at right angles through holes in the joist. When I got where I was going I nailed a board to the wall from the rim area down to where the receptacle was mounted. Staple at the top, staple a foot above the box, metal single box (with ground screw) and a 20 amp receptacle. Plastic bushing / cable clamp when passing through the knock out. Yes, I tapped off the load side of the GFCI receptacle. Also labeled the new box "GFCI" and used the screw terminals rather than backstabbing which seems to be the standard in this house