No, Bernie Sanders is not the first candidate to win the popular vote in the first 3 state primary elections or caucuses in a competitive year. For instance, as Useruser Tgr points out, Jimmy Carter won the first 3 contests in 1980 despite facing stiff competition from Ted Kennedy.
Depending on the definition of "competitive primary" used (which neither source articulates), there are potentially several more examples. For instance, as the Newsweek article itself notes, Al Gore won the first 3 contests against Bill Bradley in 2000.