Yep, the "wrong" velocity is what you suggest: the horizontal velocity is missing. Keep in mind the horizontal velocity is the critical detail that distinguishes "orbits" from "crash landings."
There is no conversion to linear momentum. The projectile is rotating once per turn of the centrifuge. Nothing they do eliminates that angular momentum. That's why in the linked video the projectile is, on close examination, rotating wildly. It's also why the projectile's nose exits the apparatus at a very different location than the tail.
I play Kerbal Space Program, so I know a thing or two about orbital mechanics! (I'm only 30% joking -- many of the answers on the Space Exploration Stack Exchange say "Go play Kerbal Space Program, then you'll understand). Yes, that horizontal velocity is hard to attain, but that's what 2nd stages have always been for. We're only talking about replacing the 1st stage, which is by far the most expensive. You're still way better off already being at orbital height, never having to accelerate directly against gravity and through all that air resistance. And the speed you need to reach orbit is less the higher up you are.
> The projectile is rotating once per turn of the centrifuge.
I keep trying to challenge this, but I think you must be right. I was thinking the angular velocity would be smaller than the arm, but it must be the same. Still, the angular momentum can be much smaller. And I'll paste my proposed (possibly infeasible) solution to that from another answer:
Attach the payload at two points in a narrow V, equidistant from the center of mass. In the instant before release, fire pistons that slightly extend the upper arm and retract the lower arm, applying the exact amount of force you pre-calculated was needed to counteract the differences in rotation between those two points. Release while this (hopefully uniform) force is still being applied.
Yeah, you're jolting the hell out of your payload, but that's peanuts compared to what it's about to experience anyway.
There is no conversion to linear momentum. The projectile is rotating once per turn of the centrifuge. Nothing they do eliminates that angular momentum. That's why in the linked video the projectile is, on close examination, rotating wildly. It's also why the projectile's nose exits the apparatus at a very different location than the tail.