Mostly what you’re doing here is balancing out the salt and acid levels of the pumpkin puree while carmalizing the sugars in it. The nutmeg and allspice accentuate the flavor and evoke pumpkin pie and since those spices are so synonymous with pumpkin in our minds, it helps make it taste “more pumpkiny”. You could also use cinnamon here, but I find cinnamon is so noticeable that it will swing the flavor from “pumpkin” to “pumpkin pie” which may not work for every dish. Everything is added in very small amounts, I’ll say. The result shouldn’t taste salty, acidic, sweet or spiced, we’re talking pinches and quarter to half teaspoons of ingredients to a 32 Oz can of puree.
Edit: there also needs to be an amount of fat for a rounded flavor profile, but I don’t mention it here because I assume whatever dish I’m adding this to usually has that component in it. I also omit parts of this process if the recipe is going to do it anyway, such as in a blended curry or soup.