There's nothing inside a motorcycle transmission that isn't also present in an automatic transmission designed around Type F ATF. Gears, clutches, you name it, they're all inside an automatic. Type F ATF lubes them just fine.
Note that all types of ATF are not the same. Type F is NOT the same as Dextron III, Mercon, Mercon V, or any of the other formulations of ATF. Some of these formulations are friction-modified, which isn't the hot ticket for wet clutches. Type F is not friction modified. I run Type F. I'd think twice before I ran Dextron III or some other type of ATF.
One other thing: in engine oil, the "W" rating is meaningless as that is related to low-temperature pumpability. Since your dirt bike tranny has no oil pump and you don't run at extremely low temperatures, that "10W" bit tells you nothing. The "40" part is the only viscosity grade that is meaningful in a dirt bike. Finally, keep in mind that the absolute viscosity (not SAE grade) of a 10w40 engine oil is pretty similar to a 75w90 gear oil. There's a big difference in the SAE numbers assigned, but not in the actual viscosities of the products. ATF viscosity is also comparable to many of these products.