Accelerating in a huge vacuum chamber seems pretty difficult to achieve, and wouldn't there be a huge shock to the vehicle as it hits a wall of dense air?

How much of a difference would a low pressure chamber make, I wonder? Maybe you could build the circular accelerator then a much longer exit pipe that runs up the side of a mountain. Although that sounds way, way easier said than done! But if your exit air pressure is roughly equal to your accelerator air pressure, then you don't need a fancy airlock system.

The tether they proposed also seems a bit too much of the wishful thinking like "we just need a bundle of carbon nanotubes 1km long!" Wouldn't an electromagnetic accelerator work better?