It's probably grounded through the 2 screw tabs. Notice the green pair of wires screwed into the metal plate lower in the picture. The noise filter might be electrically conductive between the ground pin and the two mounting screw flanges (Take a multimeter and test for resistance between them after detaching the wires from it to be sure)
In any case, if you dont have a ground pin on the cord, GET ONE. For safety alone.
Perhaps in Japan they don't use them and assume neutral == ground, but in the U.S. that is not safe for any product that has ANY electrically conductive exposed material (e.g. metal coin door, power switches, etc..).. it must all be grounded for safety.