I'm also interested in this and have done a fair bit of research.
The Retrovalves are patented, so you can look up the patent and see what's inside. I suspect they're variations on what runofgroove.com call the "Fetzer Valve", or Joe Sousa's "Trioderizer": The Trioderizer - a solid state triode
Rather than dropping the signal just to amplify it again, they probably use high voltage devices such as the LND150 or IRFxxx power MOSFETs. The LND150 is depletion mode, so it biases up just like a tube. You could almost get away with poking two of them into a 12AX7 socket.
I have a few tube-replacement circuits of my own, but they're still at an experimental stage. My approach is to have high-voltage amp building blocks that perform similarly to 12AX7s, and just string them up in a copy of a classic tube circuit, running off the same voltages. I think this works better than the runoffgroove.com approach of scaling everything so it runs off 9V.
The advantages are obvious: transistors are cheaper than tubes, smaller, quieter, don't go microphonic, don't break if you drop your amp, and never wear out. That means better reliability and lower cost of ownership for the end user.
On the other hand, making drop-in transistor replacements for POWER tubes would be a real minefield, with a real possibility of the kinds of explosions you'd expect in a minefield.
I could probably make it work using some sort of MOSFET stack in a canister covered in heatsink fins, but I think the voltage scaling approach comes into its own for the output stage. Essentially the OPT shrinks and moves before the output stage. My new hybrid amp demonstrates my work on that.