All I could afford wrote:
I have a related question as a fairly new guy here. Is it just as critical to be level when I am plugged in and running on the 120 V refrigerator? I understand why when running on the flame it is important. But to me it seems like running on electricity it won't be quite as critical especially if only slightly off level
Yes, it's just as important.
FWIW, the flame isn't the critical part.
The movement of the refridgerant is caused by the heat source and the whole process is not very strong. Therefor if your too far out of level there isn't enough force to move the coolant around and the damage begins.