Yes, the genuine does not have it, the date is set via the crown. But since this is a replica PR movement, that function does not exist therefore they had to make a quick set pusher to accomodate changing the date. Just another way of showing that this is a rep movement.
Question - what are you trying to determine?
is it rep?
is it good quality?
is it worth holding on to?
not sure what your goals are. As i mentioned before, unfortunately its not the best quality of a replica. If you want a really nice PR panerai it will cost you quite a bit. DSN has a line of PR watches that come with the correct soprod movement (As per gen) but the rotor is not engraved the way the gen is. The base movement however is the same. The rest of the watch is good (Not great or 'super' as we call them)
Your best best is to get a Noob or KW case and insert the dial hands and movement from DSN - it will wind up costing you over a grand for the combo but you will have one amazing piece.