Why does my cellular iPad not have the cellular capabilities?
My wife had an iPhone 4 for a long time and at one stage the iPhone fell in some water.  We did all the usual tricks, turn it off, put it in rice, etc.   After a few days the phone was fine and worked as normal except the wifi never worked again.

I would suspect something similar happened to this iPad.  The cellular module is probably damaged, for some reason or another, and doesn't work.  The seller most likely advertised it as Wifi Only so you couldn't complain back to them later.