Fascinating stuff, looks like it was achieved on a regular lathe with with eccentric chucks (the piece is held off-center, so it doesn’t spin about its own axis, which is where the elliptical and circular shapes come from). This fancy turning art form advanced with the invention of the straight line engine and the rose engine (https://en.m.wikipedia.org/wiki/Rose_engine_lathe), which both use cams (protrusions and depressions on a wheel) to produce consistent rhythmic alterations in either depth or displacement. This art form is more commonly known as guilloche and is found mostly on watch faces and banknote currency, where it serves as ‘proof of work’ of extreme precision and craftsmanship.
If you're interested in this, you would be remiss if you didn't check out David Lindow's work. He does contemporary ornamental turning and builds the specialized lathes to do it:
Hobby activity seems to follow what had been high-end industrial tech a few decades before. In this case fancy lathing; in the 20th century ham radio and model railroads (not to mention model rocketry); in the 21st century the "home lab".
