Google's John Mueller said in a Google+ Hangout on Friday morning that you do not need a specific desktop web site, that having a mobile site is perfectly fine. Google will rank and list your mobile web site on the desktop search results just fine. So going mobile first, or mobile-only, works perfectly fine with Google.
John answered the question at the 12:50 mark into the video:
If we have a product only & only for Smartphone so we decided to only make Mobile Website for the same (no desktop version of the site). How can we do the SEO for the same as from few articles I understood that desktop version is mandatory.
So you can have a mobile site, that is just mobile, that is just perfectly fine. That is not something where you need to have a desktop version. You can have a web site that is only mobile. It will still work on desktop browsers, of course, maybe the display will look a little bit different. But you can have a mobile only web site and that is perfectly fine then search, just like anything else.
I think what I’d try to make sure there is that it still works on desktop, that it doesn’t show an error on desktop. But rather, someone on desktop can still access it because what generally happens is we will just include the mobile site in our search results, like any other site and we will also present it to desktop users.
So make sure that desktop users can still see some of your content, if it is formatted in a way that works best for mobile, that’s perfectly fine.
You definitely do not need a specific desktop web site in addition to a mobile web site.
Here is the video embed at the start point:
Forum discussion at Google.