Why does preparing ahead and storing overnight in the fridge improve the texture of the cake?

Looking at the recipe and the headnotes, I believe the author recommends that you bake the cake immediately after completing all of the instruction steps, and then serve it the next day, if you can. That makes sense! As you suggest, going to all that trouble to beat the eggs, fold the ingredients together, etc., only to let it sit before baking would make no sense. The batter would deflate, as you've suggested.

On the other hand, desserts like this do improve both in flavor and texture when they've had a chance to sit. The flavors develop, while the texture becomes more fudge-like. Sounds good, doesn't it?! ;o)