Ok. So the exhaust is nothing, it's the fuel that's pushing the rocket up it's own arse type of thing.
Ok then tell me if this rocket would still fly and if it would, tell me why and if it won't, tell me why.
No, it won't fly, because the two thrust vectors are opposed to each other (one is pushing to the left, one is pushing to the right), thus cancelling each other out.
They're just two "exhaust" pipes into the atmosphere, you know, the one that makes no difference to a rockets propulsion.
I never mentioned the atmosphere, because it is not relevant to this diagram, or to the function of a rocket in general. Read my comment again.
Something else: try stepping off a small boat onto a jetty without mooring the boat or holding onto anything. Typically, the boat will be pushed out from under you and you will fall into the water. Why is this? Going by your logic, the water, being denser than air, should provide more resistance to the movement of the boat than the air does to the movement of your body, so the boat should stay put while you step onto the dock. Why doesn't it?