Yes. I can see why this might be confusing because in other mythologies, there might be a "god of rivers", but in Shinto, every river has its own kami. So Haku is the god of a different river.
Size isn't necessarily the same thing as power when it comes to kami. In fact a running theme in a lot of anime and manga you'll see come up a lot is that when somebody "hulks out" and gains mass in a transformation, it's more often a bad thing than a good thing; it represents a loss of the integrity of your form- ie. your human identity is lost and you have become more like a monster. A lot of the time in anime, somebody's ultimate form will be normal human sized, even if previous forms had them hulking out more and more. It represents mastery of the self- the willpower to be master of your ultimate form- your own body.