Not many motorhomes come with generators - mostly it is only high-end liners that have them fitted as original equipment. Some buyers add them as an aftermarket addition, but these are usually mobile generators that can be swapped over when they buy a new model. But no, the power is not from the engine directly, 12V power is drawn from the habitation battery or batteries for things like interior lights, pumps, fans on the heating system, etc, and everything else is usually powered by gas and sometimes diesel. If you need 240v for say a microwave or hairdryer then you either need direct 240v hook-up to the mains or an inverter and/or a generator. The habitation batteries are recharged via a solar panel, the engine, hook-up and/or a generator. If you're buying used, of course check all the electrics work first.

I was asking because most of the tips given in the video are more like buying a car rather than buying a motor home. I.e. check the exterior for dents, check the tires, check the accident report, etc. I would think that for motor homes one should check the electricals, water lines and plumbing.

The Only Used Van with a civilised running gear (As opposed to a cheap run-about) would be a Hymer or Rapido with the V6 Mercedes engine and 7 speed Automatic Transmission. Fiat is just a cheap pick-up with a posh caravan on it.