Google has deprecated the desktop Web. It's still here, but for Google it just got less important.
At least that's the implicit message in Google's recent mobile search update. The company is now judging how "mobile-friendly" a site is and is using that metric to weight search results served to mobile devices.
In case you didn't think it was important:
The only real ray of hope in there for developers who still haven't embraced some form of responsive design is that this change only affects mobile search results. Desktop searches and rankings are unaffected. So if your site doesn't work on mobile, you'll only lose, roughly speaking, 35 percent of your traffic.
I wrote about this back in January 2014 for the first time, and twice this year; once as a query and once explaining what the requirements were for a website in 2014 and onwards.
How to check if your site is responsive? You can use Google's auto testing page here. However, it's relatively easy to just open it up on a smartphone and compare - it should largely look the same only re-ordered for the narrower-width screen so that everything automatically moves down the screen. You can try it also on a computer by opening the site in an Internet Browser such as Google Chrome or Safari, then re-sizing the screen to make the window narrower - the content should re-format auto-magically to fit the width it has available. Why not try it on my own site as a perfect example!