Existing wiring is 1 red hot 1 black hot each coming into a 20 A breaker. Box has no ground. Is the neutral on this needing to be hot or do I have to run a whole new wire to new box with a ground & keep the neutral, neutral?
I don't care where that stove from, it's not being properly protected against overcurrent anyway, because uh-oh! You have a Zinsco!
Your Zinsco panel and breakers cannot provide proper overcurrent protection to anything, no matter who did or didn't test or list the appliance, so I'd replace that panel first, then go shopping at a reputable bricks-and-mortar outlet for a new cooktop, as trying to do much of anything to a circuit "protected" by a Zinsco breaker is a bad idea -- they can't even be counted on to turn the power off when you switch them off! (Generally speaking, cooktops and non-cord-connected ranges made for the North American market will use a flexible conduit instead of a cord or tray-cable for the hardwiring whip.)
Once that's done, post a new question with photos of the box in the wall where the range circuit terminates, and then we can talk about retrofitting a grounding wire to this circuit if need be. (The red/black wire pair makes me suspect this circuit might have been run in conduit.)
It looks like you are in the US, but your stove has a European style cord.
If the stove was used on a European style supply, then the L would indeed be connected to the Hot and the N to the neutral.
However, if you do that on a typical north American supply then your stove will almost certainly not get enough voltage. Most likely you will need to connect the "L" to one hot and the "N" to the other hot to get the correct voltage. This is generally safe as European/IEC appliance design practice treats the "Neutral" as being potentially live.
Ideally the manufacturer would document this sort of thing but...........
In any case ground needs to be connected to the ground connection.
Either way the ground needs to be connected