In a 2015 speech, Bill Gates warned that the greatest risk to humanity was not nuclear war but an infectious virus that could threaten the lives of millions of people. That speech has resurfaced in recent weeks with 25 million new views on YouTube — but not in the way that Mr. Gates probably intended. Anti-vaccinators, members of the group QAnon and right-wing pundits have instead seized on the video as evidence that one of the world’s richest men planned to use a pandemic to wrest control of the global health system. Mr. Gates, 64, the Microsoft co-founder has now...