Note that this is a 400 kg class launch vehicle, so much smaller than a 10 tonne level Falcon 9. Even smaller than a Falcon 1.

Beal Aerospace also tried to bring pressure fed composite launchers in the nineties, though he used hydrogen peroxide and kerosene: http://en.wikipedia.org/wiki/Beal_Aerospace

While methane has the advantage of self-pressurization, it is also about half the density of kerosene, meaning there will be double the volume for the same mass, and the pressure vessel will be double the mass. Pressure vessel mass is proportional to volume and pressure. That's why Beal used very dense fuels, even when they have less exhaust velocity.

The heavy tank is a worse problem for sea-level launched rockets that need high engine pressures to reach passable engine exhaust velocities.

The rocket equation shows that exhaust velocity is important to reach high rocket velocities: delta v = v_exhaust * ln(m_full / m_empty)

In a pressure fed rocket the engine pressure is the tank pressure (minus some pressure loss in the injector). If you air launched, it might be a bit easier, since ambient pressure is only a quarter of sea level at 10 km. Airlaunch LLC tried to use these synergistic technologies some years ago: http://en.wikipedia.org/wiki/AirLaunch

Basically in the atmosphere you exhaust at ambient pressure (or not very far from it). If your chamber pressure is low, then you can't expand much before you're at ambient at sea level. Thus the nozzle can't produce much thrust for the propellant flow. The upshot is that low pressure rockets suck at low altitudes.

But for relatively small rockets it might work well: apparently because of some minimum-gauge issues, they need to have pretty thick walls anyway so going to pressure fed is not such a huge overhead. Also equipment like turbopumps does not scale well at the low end. (I haven't studies this in detail though.)

Armadillo Aerospace has tested oxygen-methane self pressurized rockets years ago and they are simple and work well. They can also be controlled precisely. NASA bought one from them and flies it occasionally. I think it is a blow down pressurized version though (helium is filled directly to the main propellant tank head spaces for pressurization): http://morpheuslander.jsc.nasa.gov/

So auto-pressurization is nothing fancy, in fact it can be seen as a simpler version of blowdown pressurization, which is simpler than regulated pressurization.

If I had to create an orbital launcher with minimum capital, this is a reasonable design, though I'm skeptical about the aerospike.

To convince me, they need to first fly some sounding rockets.

There's been many rocket startups in the recent decades, with little flying hardware, and even that has been no guarantee of going further.