At the Oscars in 2019, one production company was at the center of the year’s most talked about films and on the cusp of the industry’s sweeping trends. The man who backed it, however, wasn’t at the ceremony.

That year the films made by Participant Media collected 17 Oscar nominations, for Green Book, which eventually won best picture and went on to gross $321.8 million worldwide; Roma, which broke Netflix into the best picture race for the first time; and Rbg, the documentary about Supreme Court Justice Ruth Bader Ginsberg that managed to become one of the highest-grossing independent films of 2018.

In an indicator of Participant and its backer, tech billionaire Jeff Skoll’s unique, dual missions, the Oscar gatherings Participant threw that year included a viewing party for the National Domestic Workers Alliance at The Jane Club, a nod to the lead character in Alfonso Cuarón’s Roma, and...