I asked on Google's forum why rich snippets weren't showing for my site to which I got a reply that they show up for rich results such as a news list or carousel. Whats a news list? Source.
"News list" and "Carousel" are special search results that Google puts at the top of the page. Rather than being search results for general web sites, they offer results curated from specific categories. Other similar treatments are OneBox, Plus Box, Direct Answers & The 10-Pack.
The news list lists top stories from recent news reports that are related to the query.
Carousel search results are a long bar at the top that scrolls right. Google uses that treatment for things like lists of hotels.