I will add that their numbers look different from work I've seen before, and use a more ambitious methodology than I would use. They want to run the entire launch using the magnetic system. This has some serious issues that make it harder IMHO - not that I know much. I believe it would be much easier to justify, finance, and build a system that replaces most or all of the first stage, which is where about 90% of the mass and propellant is spent. Just getting to Mach 5 uses up to 90% of the required fuel at present. It would also eliminate the entire cost of the first stage, replacing it with the cost of electricity, plus wear and tear on the magnetic launch carrier (which could be re-used.)
This approach would not require the high 30G acceleration (which eliminates use for living things) nor the super-long 130km launch track of the MagLaunch system. It would be cheaper and easier to build. This would be a 5G to 10G system with a 50KM track, going up the Andes at the Equator to an elevation of as much over 14,000 feet as can be arranged, with a 5km/s exit velocity if I recall correctly - this would require some work to make a vehicle that could survive such high speeds at relatively low altitudes. At 14,000 feet the air pressure is about 1/2 STP, and at 28,000 it's about 1/4 but there's no satisfactory location that goes to 28,000 feet. But this is getting into highly speculative numbers.