I was under the impression that it was illegal to have any kind of light emitting signage on a moving vehicle. Does this vary by jurisdiction?

Everything to do with cars varies by jurisdiction..

Difficult to work out what the law is for side visible displays is in the UK, though. Front and back ones may be limited to white or red.

I'm now wondering how camera only self driving cars are going to cope with this, too.

For trucks, it varies by the trip. There is county/locality, state and federal jurisdiction.

Operators are adept at gaming the system. From Chinatown busses that use sequences of shell companies, to operators who operate out of friendly locales in a limited radius.

Yes. Video trucks are already common in Las Vegas, NV, USA.