"This can cause issues when the mobile page has less content than the desktop page because our algorithms are not evaluating the actual page that is seen by a mobile searcher". But this Google announcement makes it sound like the process of mobile-first indexing on a larger scale has already begun.
Until now, Google used content from a page's desktop version to index and rank websites, but switched links at the last moment to a site's mobile page if the user was searching from his mobile device. Google said that they'll increasingly be indexing the mobile version of sites over the desktop versions, but relevant searches are the primary goal.
Google announced this morning its "mobile -first" index of the web is now starting to roll out, after a year and a half of testing and experimentation. Google does mention at the bottom of the press release that "having mobile-friendly content is still helpful for those looking at ways to perform better in mobile search results". However, some sites have significantly different versions of content for desktop and mobile browsers, the latter often a watered-down copy of the former.
Don't call it the mobile-first index, but rather call it mobile-first indexing.
Those sites who have been shifted will be notified via Search Console, says Google, and will begin see increased visits from the Smartphone Googlebot.
Google said it took this decision because most of its search traffic comes from mobile devices and its search engine should also reflect the current situation.
Let me know if you see a cache show the mobile version of a site, that is a strong signal that site has moved over!
Things won't change a lot on Google Search Desktop, where content from the desktop versions of pages will continue to surface in search results as they did until now. For example, there are times when a non-mobile friendly page still has the best information and will appear higher, Google says. Being indexed this way has no ranking advantage and operates independently from our mobile-friendly assessment.