Thank you for posting such good photos.
The object is in the shape of an uchide-no-kozuchi, the magical mallet carried by Daikoku, one of the seven gods of luck. According to legend, swinging the mallet brings luck and grants wishes, so it would have been a very appropriate presentation gift.
If the object is in fact a box, its most likely intended use was as a kogo, the small incense box used in the tea ceremony. This mallet-form box was fairly popular and was probably marketed by other retailers as well as by Mitsukoshi.
Motoda Hajime (1858-1938) was a lawyer and prominent politician, first elected to the Diet (the Japanese Parliament) in its inaugural session in 1890, eventually serving as Speaker of the House of Representatives of Japan. He was appointed to a string of ministerial posts, including first Minister of Railways from 15 May 1920 to 12 June 1922. I believe the jubilee marked the fiftieth anniversary of the establishment of the first railway in Japan, although passenger service probably only began the following year (1872).