I'm not a rocket scientest but doesn't the curvature of the Earth come in at some point?
It comes into play very quickly, but we already hit objects that are hidden by the curvature of the Earth.
Gravity ensure that the projectile comes back to Earth, unless you put it into orbit. Remember that the first abort runway for the space shuttle leaving Florida was the Azores (over 2000 miles away).
I believe essentially what he's saying is the gun could place a ballistic object in almost LEO. Personally, I think anything travelling 2000mi is going to see substantial effects from wind resistance. Guidance is easily dealt with, with modern electronics and GPS, but your terminal approach after travelling that far is not going to be as great I wouldn't think. Then again, dropping large rocks from space is a pretty potent weapon as well. (See The Moon Is A Harsh Mistress)