It should read " a small house on the seaside"...just a typo.
It is better than saying 'a small house at the seaside' or 'a small house by the seaside', isn't it?

Nope, at the seaside is the best one, by far!

'On the seaside' is wrong. By contrast, 'on the side' is correct.

http://www.audioenglish.org/dictionary/on_the_side.htm