It is the base that is the important thing, not the visual model. The base of the model is moving, thus the whole model is counted as moving. You cannot have different parts of a model moving or not moving, otherwise wouldn't that same logic apply to chariots? Most of their crew have bows. Or what about standard cavalry? Technically the mount is moving but the rider is not, ruleswise the model is moving.
Even though the howdah is bigger, think about the amount of wobbling and movement you are going to get on it with the steg lumbering along, not exactly easy to aim a weapon straight.