Nigiri-zushi is a specific version of Japanese sushi that has a slice of raw fish on top of a bed of rice. This is what most Westerners think of when they think of sushi. This version, which came into being around the early 1800's, is the most recent version of Japanese sushi, which was introduced in Tokyo (formerly called Edo until the Meiji Restoration of 1868). The key factor is serving *raw* fish, which was only possible through relatively modernized transportation and distribution system. Therefore, nigiri-zushi is also referred to as Edo-mae-zushi.

Your recipe is most definitely *not* nigiri-zushi. It looks like what we Japanese would call "yaki-onigiri", which basically is a grilled rice ball. Also, we usually reserve the term "rice cake" for "mochi", which essentially is made by molding cooked glutinous (short-grain or sticky) rice pounded into a paste.

FYI, sushi has been an integral style of Japanese cuisine for nearly 800 years. Different regions have their own sushi (Kyoto, Osaka, Fukuoka, etc.) and each household boasts a sushi recipe that's been handed down through each generation.