If you follow a line down from it you can see that the pylon below it is slightly wider than all the rest. It seems to have a pipe attached to it.
It must have been to pipe fresh water, either from a well or more likely a pipe leading from shore to that hut.

In any event it is not the sort of windmill one would use for generating electricity. They had been developed in Denmark about 15 years before this but they were MUCH larger.
from 1889:

On a pier. Why?

[Generate power for whatever goes on in that building? -tterrace]

Okay, that guy in the front helping his son (daughter?) navigate the waves is a definite hottie in my book (the biceps alone--woweee). Rather tricky to deal with a crush on a man over 130 years old though, so I will just admire how he nicely fills out his bathing suit from a distance -- a very loooong distance.