Right on the machineguns. My bad, I had the Type 92 (Hotchkiss type HMG), and the Type 99 ("Jap Bren"), reversed. Anyway the 7.7 semi-rimmed was made for the Hotchkiss type and that is what is in those feed strips.* The latter took the same rimless round as the Type 99 rifle.
Sport45, the confusion comes because the Japanese used the date of adoption, as the U.S. did until the 1930's. Every firearm adopted in 1939 (2599 in the old Japanese calendar) was a "Type 99". As Mike says, a Japanese saying "Type 99" would have to say "Type 99" what. We have the same problem with, for example, Model 1917, which could be a rifle, one of two different revolvers, or a Browning machinegun.
*Edited to add that I just looked at the box and even I, with almost no Japanese, can read "Type 92".