Pinterest works for the average Pinterest user primarily because it fits into the metaphor of the site (items pinned on a bulletin board) and therefore enhances the information architecture of the site. This acts as a functional multiplier across the entire site. The fact that the content is visual falls out from this but is not necessary; many pinned items are actually primarily textual. Sign up flow, email notifications, etc are tertiary.

Generally, a non-traditional layout (where traditional is flat list or tree-based) should be chosen if it is compatible with or can even reinforce the information architecture. E.g. if you're site is based on the idea of building a house out of bricks, a 'mason' layout would work :)