The watch is one of a range called the Nintendo Wrist Watch In A Cube Case. This was a series of watches by Banpresto for Nintendo commemorating the original 80s Nintendo products. The watch is indeed housed in a Cube case, with the watch mounted on a cross shaped plastic holder. Banpresto is a Tokyo based toy company and is now a subsidiary of Namco Bandai (although it was only partly owned when this watch came out). This brand now focuses on the prize machine toys.
The watches were made as prizes for the UFO Catcher machines which are game machines that allow you to catch a prize (usually by controlling a moving claw).
This watch is the Nintendo Disk System model. It celebrates the disk drive add-on for the Family Computer (or Famicom or Nintendo Entertainment System). This system was only released in Japan, and gave access to use double sided 2.8x3" disks which had a capacity of 112kB (56 per side). The face of the watch shows the mascot for the system (called Disk-kun), along with the name.
The watch itself is a small 3 - handed dial, and was released in 2004 (which is actually when the original Nintendo support for the disk system ceased).