Military is a designation. You need to be reporting to the military command and administratively be under MoD to be considered military. NSG is technically a federal CT unit under home affairs. Doesn't matter how militarized they look or where they draw their personnel from.
Labelling such units as military or paramilitary is not good. It sends a message that law enforcement capabilities in a given country are bad therefore required military to step in. That's a hallmark of failed or fragile states.
That's why I'm even against CISF wearing camouflage at airports. First, their stupid desert camo is useless in that urban environment and secondly anyone coming in thinks they're military. Military does not guard civil infrastructure unless something has gone horribly wrong or security situation in country is extremely bad. Unfortunately the jokers in MHA do not understand perception management.
And the label 'paramilitary' is also bad & wrong and sends the wrong message as that term usually describes a unit operating outside its usual mandate that would be on shaky ground under international law. Sicarios contracted by a Latin American govt to combat cartels can be considered paramilitary. CIA Ground branch can be paramilitary. But FBI HRT is not paramilitary and neither is NSG. They are official govt agencies operating under specific mandate of law.
India does not have any paramilitary unit with the vague exception of SFF/SG.
We only have CAPFs which are best described as Armed Police.