With neither sanitation, nor cooking, nor (apparently) a permanent AC electrical system, I think this wouldn't get classified as a motorhome in most states, but simply as a plain old truck.
That said, the class A/B/C system is not absolutely perfect, particularly for homemade or custom creations. In as much as the body appears to be added on to a cutaway, I think this would best be described as a class C—as much as anything. (It doesn't look quite like a standard van body grafted onto a longer chassis, due mainly to the lack of wheel wells, but quite possibly it is and the wheel wells are merely filled in with sheet metal or something.)
A school bus conversion is another sort of RV that is somewhat hard to classify. I guess most would put it down as a class A, even though logically it is closer to a really large class B in terms of who built the body structure.