Maybe a silly question, but I've been trying to learn a lot of baking fundamentals and trying to understand specifically what makes a cake. Most explanations I've read are something along the lines of:

• flour for structure


• fat to interfere with gluten development


• sugar for taste and moisture


• binder (eggs) to keep it all together

Then the explanation for the flour is that the water and flour interact to produce gluten that then gives the cake its structure. One main thing doesn't make sense to me here though:

If flour is there for the gluten, and gluten is required to form the structure of cake, how can gluten-free baking ever work?

Now, I've done gluten-free baking plenty of times. Have never really had an issue. Additionally there are tons of alternatives, how can you get something cake-y out of so many different materials, none of which have gluten? Are there alternative protein networks that function like gluten? Are these protein networks common or rare, or beside the point altogether?

Not sure if it's related, but why does adding xanthan gum to these gluten-free flours seem to always make them better?

Then the explanation for the flour is that the water and flour interact to produce gluten that then gives the cake its structure.

Your confusion is reasonable, because

gluten is required to form the structure of cake

is too strong of a premise. Gluten can be the primary contributor to the structure of a cake (for example, consider the wacky cake), but there are other ingredients that can provide structure.

This answer limits its scope to cakes and does not discuss other forms of gluten-free baking (bread, pies, etc).

Structure Provided by Egg Protein

Angel Food Cake

As noted in this recipe for angel food cake by Stella Parks, egg white can provide sufficient structure for a cake.

... angel food cake is so high in protein from egg whites, it has enough strength to stand on its own ... With that kind of underlying structure, all angel food cake really needs is enough starch to keep its moisture in check

Note that the motivation behind removing gluten in this recipe is specifically avoiding the additional structure gluten provides:

angel food cake toughens up like shoe leather in the presence of gluten

Brownies

In my personal experience with a few brownie recipes, protein from eggs provide a considerable amount of structure; omitting eggs without adding protein produces dramatically different results.

The most rigorous experiments that I have performed were attempts to replace eggs in this recipe for brownies by Alice Medrich.

Key Observation:

Replacing AP wheat flour with rice flour wile still using eggs produces a brownie. Omitting out eggs (without adding enough hydrated protein) produces something that is definitely not a brownie.

When eggs are replaced with water, lecithin, and starch, the recipe produces a sticky, caramel-like mass that separates from a significant amount of oil. This was observed with rice flour, gluten-free flour with xantham gum added, and AP flour.

Other observations:

• Whey protein isolate mixed with psyllium, starch, baking soda, and water is the best substitute for eggs tried so far. It produces a crumb similar to that observed when using eggs.


• More gluten (in the form of vital wheat gluten) mixed with flaxseed, psyllium, and water also appears to work as an egg substitute, but note that this egg substitute involves hydrating the substitute for 10 minutes before adding it in the step of the original recipe where eggs are added. Even then, the produced brownie is softer and less airy than one produced with whey protein.
  
  
  • I do not expect this replacement to work if the dry ingredients of this substitute were simply mixed into the other dry ingredients (flour and salt) before mixing wet and dry ingredients.
  
  

Weaker evidence: This recipe by Dandelion Chocolate appeared to work fine with AP flour replaced by an equal amount (by weight) of rice flour.