There is a major difference though, in that book they use a long linear catapult. This helps keep the G force down (in fact it's low enough that humans can attempt to use the catapult to travel). Making a second stage for orbital maneuvering that can withstand that kind of acceleration is not particularly hard.

What spinlaunch is proposing is to use a fairly small circular catapult. The G force involved in that case is huge, something like 4 figures. We can make electronics that can survive that (although this is close to the upper limit), but can we make rocket engines and fuel tanks that sturdy? Personally I doubt it.

That was a linear driver on the moon. It's closer to The Man Who Sold The Moon, but that's also a linear driver up the side of a mountain on earth.