Those doors could lead to big improvements in the space program, as well as in terrestrial travel. The more immediate benefits would be to the space program, and they could be huge. These new aircraft wouldn't totally replace rockets, though. They'd only replace the first one or two stages of the typical launcher, the ones that work within the atmosphere. Combustion requires fuel and oxygen.
Rockets have to carry both.
They pluck their oxygen right out of the atmosphere. So air-breathing craft of a given weight could carry a far larger payload than rockets of the same weight. That could make it possible to put much bigger payloads in orbit, or to put them up there a whole lot cheaper - or both, which is how NASA views things. You'd still need rockets for the final parts of any mission, of course, the ones that occur above the atmosphere. However, up to that point, it would be air-breathers doing all the work.