schema.org – Google – rich search results appear but no structured data

I was wondering if there’s a way to get google to display rich text results without implementing any kind of structured data.

When google displays a link to a page, it may also display some extra information under the link. This is what google refers to as “rich results”. So, for a product page, it could list things like warranty information, rating, price, brand, etc.

I came across a search result for a website that displays some of that extra information, but when I scanned it using Google’s Rich Results Test tool, it didn’t seem to have any kind of structured data, and it says “the page is not eligible for rich results”.

This is rather puzzling. What am I missing? Is there another way to indicate to the google crawler which information to use? Do I absolutely have to implement Google’s structured data in order for these extra bits of information to appear?