How does gumbo spoil while still cooking?
I believe in this context, spoil is not referring to food safety issues such as dangerous pathogens, but rather that the dish does not fulfill its culinary promise.

For example, any soup or stew that is cooked on too high a heat will become burnt on the bottom. You won't get sick from eating it, but from a flavor aspect, it's spoiled.

Not being an expert in cooking gumbo, I can't cite all the specifics, but there surely is an optimum heat and time that it should be cooked. Stray too far from the base recipe and technique, and you may spoil the gumbo.

From your comments, it sounds like the recipe calls for cooking the gumbo to a point of "doneness", and then turning down the heat so that it stays below the boiling point. In other words, if the fully cooked gumbo continues cooking at a full boil, the recipe will be spoiled.