As a Googler, I can tell you that no one I know here is under that impression. (Your instincts are absolutely correct.)

Desktop and server processors, and desktop operating systems.... Microsoft and Intel. Somewhat similar in that the platform itself is not growing as it once was, though still large...and that innovation has slowed.

Edit: Yes, mobile is hitting desktop, but that's the market itself changing...not the market share for desktop. Comparable in the search space is more people using Amazon directly for product searches versus starting with Google. Related markets and effects, but Amazon isn't a general search competitor.

Microsoft is rapidly losing the entire market of "Desktop" to Android and iOS apps. Intel has a serious competitor in ARM; most $bigcos haven't switched yet, but are definitely looking into it, as a way of applying pressure and keeping Intel's costs down.