Preheat oven to 400 degrees F (200 degrees C). Prick each potato a few times with a fork and place on a baking sheet.
Bake in the preheated oven until tender when pierced with a knife, about 50 minutes. Cool until easily handled, about 10 minutes.
Peel potatoes and pass through a ricer or food mill into a large bowl. Make a well in the mashed potatoes with a wooden spoon and pour in egg; mix well.
Whisk potato starch, sweet rice flour, and salt together in a bowl. Sprinkle over potato mixture; stir until a soft dough has formed. Cut dough into 4 equal parts with a knife or pastry cutter.
Dust work surface with rice flour to keep dough from sticking. Roll out 1 piece of dough into a rope about 1 inch in diameter. Cut into 1-inch gnocchi. Gently roll each one with the back of a fork to create ridges. Repeat with remaining dough.
Shake off any excess rice flour and let gnocchi rest, about 5 minutes.
Bring a large pot of salted water to a boil. Add gnocchi in batches and cook, without stirring, until they float to the top, 1 to 2 minutes. Remove with a slotted spoon.