For many years, those who work on accessibility have been saying that Google (and other search engines) are "blind." As a result, Search Engine Optimization (SEO) and accessibility work together to enable users to find information and access it successfully.
The idea is that a search engine looks at a web page in ways that are similar to a screen reader i.e. it looks for a page title, meaningful and consistent use of semantics, and a logical page structure. While these concepts remain true and can help make the case for accessibility, Over the years, Google, like screen readers, has become more sophisticated.
Nevertheless, it remains important always to consider Progressive enhancement when you are developing a Web site or application. Progressive enhancement helps everyone to at least be able to use the minimum functionality in what you build, regardless of device, available band width, etc.
Making captions and transcripts available with your videos can help with SEO since there is text for search engines to examine. 3Play Media, a third-party vendor, has a number of blog posts related to Video SEO that present evidence to support these ideas.
For a more detailed overview of the partnership between SEO and accessibility, WebAIM's article Web Accessibility and SEO is one of the best places to start. Highlights about how SEO and accessibility align include:
Note the WebAIM article provides much more detail, so it is worth a closer look.
While, at the time of posting this page, Google had just begun Rolling out the Mobile-friendly update, it is safe to say that the information in the Webmaster's Mobile Guide is unlikely to harm accessibility. In fact, the expectation is that attention to and increased visibility of the mobile experience will benefit everyone.