Larry Page is not a typical chief executive, and in many of the most visible ways, he is not a C.E.O. at all. Corporate leaders tend to spend a good deal of time talking at investor conferences or introducing new products on auditorium stages. Mr. Page, who is 42, has not been on an earnings call since 2013, and the best way to find him at Google I/O — an annual gathering where the company unveils new products — is to ignore the main stage and follow the scrum of fans and autograph seekers who mob him in the moments he steps outside closed doors.