That was sort of how C.S. Lewis imagined Mars in Out Of The Silent Planet, before we really had a good idea of what Mars was really like. Most of the planet was unlivable without an air supply, but the valleys trapped enough air for plant and animal life to thrive.

If one were to make a hole like the one described in the video, I wonder how much that would affect the atmospheric pressure on the rest of Mars?

Interesting idea, but wouldn't the ejecta from multiple impacts create a global cooling effect, which would be counterproductive to the intent of the project (i.e. a warm, high pressure area)?

Interesting. So maybe the asteroid that killed the dinosaurs was an alien attempt to make earth habitable for them.