The article states the company in question is only trying to achieve somewhere between Mach 1.6 and Mach 5. It will need a rail miles long, but more importantly the bulk of the velocity change needed to get to orbit will come from rockets.
It takes 9-10 km/s of delta-V in a real world scenario to get to low earth orbit. That’s about Mach 27 or so, a long ways away from Mach 1.6 or even Mach 5.