You seem to be under the impression that only potato starch can replace the wheat starch provided by wheat flour in standard recipes. This is a misconception - any starch will do, and besides, the more other carbohydrates you have (sugar, fibre), the less starch you need, as they also store moisture and are to some extent interchangeable in this function. The other ingredient that gives cakes a moist mouthfeel is fat.
So, to look at your ingredients:
- nut flour: has starches, fibre and fat
- rice flour: that's pure starch
- 1g xantham gum: a fibre, but not directly connected to moisture (it is used for the leavening to work)
- water: beside liquid-retaining ingredients like carbohydrates, you also need the liquid
- coconut sugar: sugar
- coconut oil: fat
- cacao: starch and fat
- salt: doesn't contribute to moisture
- cake yeast: doesn't contribute to moisture
- vinegar: same as the water
- sweet potato: not only is it full of starch, sugar and fibre, the fibre is in the form of already-hydrated hemicellulose and similar, which is excellent for a moist texture in baked goods.
So, at the end of it, most of your ingredients work the way you assumed potato starch should. In fact, some of them are also used in wheat-based recipes in order to make the cake moister, since they work better than pure starch.