Existing wiring for electric range

Absolutely correct for that type of configuration. The NEC does not have a wiring code except for a couple of situations that you do not need to be concerned with, in the residential arena. Using a white wire as a hot is very common especially with 3 wire cable, for 240 volts. It is common for the ground to be smaller than the conductors in your situation.

Make sure everything is tight and be at peace with the world.

At least about this, humor

Not "absolutely" correct. The NEC requires an insulated ground in this case since it will be carrying the neutral current from the control and pilot light circuit which operates at 120 volts. Also it is only going to work if it is landed in the service panel and not a sub-panel, since the neutral and ground would be separate in a sub panel. A correct configuration therefore, would likely be a black, red, and a white for a 3 wire plug. Current code requires a 4 wire plug with separate ground and neutral, which would be a Black, Red, White, and a bare ground. If your plug was installed prior to this requirement, it is likely to be "Grandfathered" in, depending on local code.

P.S. , The white wire is required to be colored by paint or other indelible means, (not tape) , if it is landed on a breaker. A white wire is a neutral, according to the NEC.

Don't they now use a 4 wire cable? Black and Red for power, White for return and a bare ground.

Yep. It was earlier on when they used that config. Once upon a time you didn't have to ground switches or recepticles either.