Google warns site owners that their site is not mobile friendly in mobile search results when they are signed into Webmaster Tools and they're the owner for that particular domain.
It looks like Google have gone to a fair bit of trouble to force websites be mobile friendly. Warnings were sent out last year to individuals via Webmaster Tools, they then announced the update. Now they're warning site owners, so i'm thinking that the update due to release in the coming days (April 21st 2016) may cause a bit of a stir. To be honest if you don't have a responsive site now and your aim is to convert visitors then i really do not know where you have been the last few years. You'll be losing business guaranteed, whether that is sales, leads or whatever the aim of your website is. So it only makes sense to make it mobile friendly before you move down in the rankings and i imagine it will be harder to climb back up even if you fix it after you've been hit. Google makes out it only really affects your mobile rankings, but you can never be too sure as having a responsive site will improve your experience not only on mobile but on tablets also.
Jennifer Slegg has an old site that is not mobile-friendly, and she reported that when she views the site in the mobile search results, it says to her in the snippet, “Your page is not mobile-friendly.” That message is a hyperlink to a Google help page about mobile-friendly.
Here is what Jenn sees as the site owner of a non-mobile-friendly website:
Here is what anyone else would see for this site — no warning:
This new warning comes a month prior to Google boosting the mobile-friendly algorithm.
One of the best ways to prepare is to test that Google considers your web pages to be mobile-friendly by using its Mobile-Friendly Test tool.