This is an example of a branch of figurative language called personification. Clearly, the moon cannot walk in the way that living creatures are able to walk. Walter de la Mare is writing in a non-literal sense in order to create an impact on the imagination of his reader. I think that is choosing to describe the effect of the moon on the earth below it in this way the poet creates a deeper, emotional, response in his readers.
In fact, as the earth turns on its axis the moon does appear to move across the night sky. But describing this movement figuratively brings a tone of mystery and magic to the lines, creating a vivid impression that the moon is alive and seeking out features in the dark landscape.