The problem with turbofans (the most efficient jet engine at high subsonic speeds) is the fan, compressor and turbine have different optimal speeds. (The fan wants to spin slow to promote a high bypass ratio without tearing the blades apart while the compressor and turbine want to run at full power.)

The conventional solution is additional compressor and turbine stages. The novel one is the geared turbofan. Both, to my knowledge, are tuned for a specific airspeed and altitude. What these guys seem to be getting at is driving the compressor separately. That doesn't decouple the turbine from the fan, but if they're racing to Mach 3 and then dumping off, they don't need a fan. Altogether, there is an efficiency threshold past which a turbojet first-stage (probably rocket-supplemented) makes sense.

Where I'm sceptical is in choosing launch as the beachhead. If you have a better turbojet--particularly one pitching efficiency over thrust--you should be building drones. Probably missiles. You'll get more build opportunities at a smaller scale, lengthening your runway and speeding up your learning curve. You have more customers and a cleaner path to export. You get to segregate the subsonic and supersonic markets in engineering time and capital deployment. The only reason to go for space first are passion over practicality, a need for vaporware-insensitive investors or an additional design advantage not yet disclosed.