Can you make a CPU out of electronic components drawn by hand on paper?
If the gain of a single inverter is less than unity, then it will not be possible to combine any significant number of gates together to build a larger circuit. The signal levels will just peter out.
To be viable, a circuit for building logic needs to have output signals that are compatible with the input of the next gate. At first glance, your inverter has a 0-12 V input swing, but a 6-15 V output swing. The voltage gain is 0.75, and there's also a significant offset.
I found a copy of the paper here. In it, they provide the following graph of input vs. output voltage. It turns out that your notation of an output-low voltage of 6 V is overly optimistic — it only gets down to about 7V, achieved when VGS exceeds about 40 V! Even if you drove your first gate with the full 0 to 40 V swing, its output would only go from 13 down to 7 V. If you then try to drive a second gate with this signal, the output of that gate wouldn't budge at all!

Furthermore, with the very high impedances involved, the clock speed would have to be extremely slow — probably on the order of a few Hz. Which would be fine for a demo, but not much else.