The buns are made with glutinous ("sticky") rice flour, which is more often found in steam buns and desserts (they also happen to look like steamed buns, except with a bit of browning).
The glutinous rice hamburger is actually a pork burger with a ketchup and vegetable based glaze, while the glutinous rice hot dog comes with a pork sausage. The hamburger is 330 yen (~$3.24 US), while the hot dog is 360 yen (~$3.53 US).
With an increased demand for gluten-free products here in the U.S. of late, it'll be curious to see if any U.S. fast food chains try their own gluten-free buns.