"The theremini is digital, I think...I don't actually own one." - flounderguts
Yes, the sound synth engine is entirely digital. I believe the antenna signal is analog heterodyned with a DSP clock, and then processed digitally.
"There are plenty of digital theremins, though...probably the most popular is the the Open Theremin V3, which runs on an Arduino Uno."
Yes again, but the heterodyned signals are generated external to the processor.
"There is also the Burns Zep,"
This is almost certainly analog, using digital components in analog mode.
"the Glasgow Digital Theremin,"
Same, some digital components in analog mode.
"the D-Lev FPGA theremin"
More digital than any others out there that I'm aware of, even the antenna oscillators are largely digital.
"I'd guess that the Doepfer A-178 is another one that there are a lot of...but people who do not dabble in Eurorack have probably not heard of it."
From the pix on the web it looks analog to me. It appears to have an LC oscillator, probably more like the volume loop on the Etherwave.