The mass of the air in the shuttlebay may be 6,000 tonnes but the mass of the Enterprise is around 4.5 million tonnes.
Yet the Enterprise does move sufficiently far to avoid the collision, with the shuttle bay's atmosphere as the only propulsion.
So consider, part of the impulse drive includes "space-time driver coils
" that reduces the Enteprise's mass, thus making it possible for the impulse engine's thrust to move the ship. Now from dialog the impulse engine were not producing thrust (neither were the maneuvering thrusters) , but if the driver coils themselves were still in operation, this would enable the thrust from the shuttle deck's open doors to move the Enterprise.
Again, the Enterprise does move.
But, that's giving them the credit of the mass-reducing coils operating. If they're not there's not enough mass being expelled from the shuttlebay to move the mass of the ship. Equal and opposite reaction. 6,000 tonnes is not equal to 4.5 million tonnes.
The air in the shuttlebay can only move 6,000 tonnes, its own mass. It might slightly ever nudge
the ship a teeny, tiny, iota of a bit. But certainly not to move as much, or as quickly, as we see it move in the episode.