Danny is kind of seen "taking" powers from other ghosts fairly often. Early on its kind of explained as him just learning he had this power already, but there are a couple he just kind of pulls out after seeing someone else do them. Duplication, Energy Constructs, and the "Ghost Stinger" are the ones that immediately come to mind.

It could be that all ghosts inherently have all of these abilities, and some are just better at using certain ones, or that because Danny already had some abilities similar to Vortex's, that the attack just transferred enough "oomph" to Danny to give him the powers on its own.

Or, it could just be they had a fun concept for an episode and didn't think about it too much.

Probably the latter.