help understanding this recipe gluten free and vegan The recipe is:
75g nut flour
55g rice flour
1g xantham gum
100g water
120g coconut sugar
30g coconut oil
20g cacao
1g salt
6g cake yeast
10g vinegar 
125g sweet potato 

I don't understand how this recipe works (and it works because I baked it) without potato starch or other ingredient that provides moisture to the cake. Can someone please explain to me the thinking behind it?
You have several oily ingredients like coconut oil and nut flour. Oil is one of the 2 ingredients that make a cake moist and it helps retain the moisture. The other is simply water.
In addition to plain water there is xantham gum in the recipe. Xantham gum binds a lot of water and retains it, keeping the cake from drying out. That's why only 1g of it is needed to incorporate 100g of water into the cake. If you leave the xantham gum out of the dough, the cake would probably be very soggy if it wasn't baked long enough or too dry if it was baked for too long. Hitting the perfect spot between soggy and dry would be much harder and the cake would dry out within a day or two after baking.
And lastly there is rice flour and sweet potato. Both of them contain starch (and the sweet potato also adds a little more water to the cake). When starch gets cooked (or baked in this case), the molecules swell and can retain moisture much better than uncooked starch. You can see the effect when cooking a pudding / flan / blancmange.