I think this is less a case of the ROF of the guns and more a case of which synchonization technology is used in a particular ride. The WW-I rides are all mechanical / cam synchronized, but since the guns were all in the 450rpm range, and you had props turning in the 1200 rpm range (on a rotary, more on an in-line engine) - this was sufficient to give you full ROF on the guns.
By WW2, the guns are firing faster, the engines are turning much more rpms, so they have a variety of different syncho methods they use. This sounds to me like the Ki-61 was using an older mechanical syncro system instead of one of the newer synch gear or electrical systems.
If you want to check out a cool synchro system, do a search on the british sonic system.