In my opinion the video does not obviously show as large of a wobble as one would expect from the shared photos. A handheld camera makes it difficult to tell. It is still possible to have the appearance of the hub of the pulley seem off, and the actual V groove spin true - depending on the jig. Fran - you are definitely correct that the "tower" of the pulley is not centered but it doesn't need to be for the outer portion to run true.
The only real way to tell is to mount a dial indicator or similar and check the runout at the outer part of the pulley. You could also make a small pointer and bolt it through one of the water pump bolts, and measure the delta between pointer and outer pulley carefully at many points. It is possible the center "post" of the tower is not actually centered vs the V groove in the pulley. The way these are usually manufactured, the jig holds the outer pulley and spins for the weld so it will run true on the belt. Does it look suspect? Yes, but it may actually be OK.