For a native speaker, "water spout" is likely associated with a water pipe or a drainpipe, especially because of the famous children's song "The Itsy Bitsy Spider", where the spider climbs up a "waterspout."
The word "waterspout" traditionally refers to a pipe or structure that directs water away, such as a drainpipe on a building. Over time, especially in nursery rhymes and casual usage, it became synonymous with a vertical pipe for water drainage. This cultural context likely influences why "waterspout" brings to mind a pipe rather than, say, a natural whirlpool or tornado over water, which is its other meaning.
So, the association comes from cultural context and language evolution, not strict logic.