The question focuses closely on the activities of the director that occur when on set shooting the movie, but this is actually quite a small part of the overall activities of making a movie. The overall process might be years long, with only a few weeks or months shooting 'film'.
To quote from the first few lines of wikipedia's definition of Film Director:
A film director is a person who directs the making of a film. Generally, a film director controls a film's artistic and dramatic aspects, and visualizes the script while guiding the technical crew and actors in the fulfillment of that vision
This is absolutely no different for an animated movie from a live action movie - the director controls the entire artistic and dramatic aspects of the movie - from refining the script and casting actors through to the final refinements of editing, sounds and effects. However as @MeatTrademark says, the set and cameras and replaced by artists.
For more specifics of the role that the director performs on an animated movie, see the following article on slate.com. This article states that a director of an animated movie has even more control over the creative process than a live action movie because of the unlimited ability to micromanage every frame of the movie, and argues that an animated movie is more of a single person's vision than a live action equivalent.