In Europe, you can buy frozen desserts; ice creams and sorbets at stores or order at the ice cream parlors. If you buy at the ice cream parlor, you can take away and eat during your sightseeing.
On the other hand, in Japan, soft serve(soft ice cream/soft cream/soft ice) is much popular than normal ice cream with bars or cones and therefore ice cream parlors selling various flavors can be found less than in Europe. However, soft serve is hardly to get at supermarkets or convenience stores, therefore if you want to eat at your hotel, you have to buy something different.
The photo is a frozen dessert called Shirokuma, which means White Bear in Japanese. Shirokuma is a popular frozen dessert which includes shaved ice, various fruits and sweetened condensed milk. This one is sold at Seven Eleven Convenience stores but Shirokuma is originally from Kagoshima in Kyushu, where you can eat at cafes and diners throughout Kagoshima.
Not only sushi and tempura, you should not underestimate the quality of Japanese frozen desserts!