Mr. Stuber, armed with Netflix’s debt-financed war chest, has films coming from Martin Scorsese, Steven Soderbergh, Dee Rees, Guillermo del Toro, Noah Baumbach and the king of spectacle, Michael Bay. “If you’re going to build a great film studio, you have to build it with great filmmakers,” Mr. Stuber said, noting that Hollywood royals — Meryl Streep, Ben Affleck, Eddie Murphy, Sandra Bullock, Dwayne Johnson — had also signed on for Netflix movies.

Mr. Stuber’s operation is set up to supply 55 original films a year, including some with budgets as high as $200 million. Add in documentaries and animated movies, handled by other divisions, and the number of annual Netflix film releases climbs to about 90. To compare, Universal, one of Hollywood’s most prolific traditional studios, releases roughly 30 movies a year.

Until now, moviedom has been relatively protected from the digital forces that have reshaped the rest of media. Most films still arrive in the same way they have for decades: first in theaters, for an exclusive run of about 90 days, and then in homes. Multiplex chains, including AMC and Regal, have fought off efforts to shorten that period. They worry that people will be reluctant to buy tickets if they can see the same film in their living rooms just a few weeks (or days) later.

“Given the marginal profitability of the theatrical business, if you lose 10 percent of the audience — some people stay home — some cinemas go out of business,” said John Fithian, president of the National Association of Theater Owners, a group whose members believe big screens are part of the very definition of film.

Netflix mostly bypasses theaters. To qualify for awards, a handful of Netflix movies appear simultaneously online and in art theaters in New York and Los Angeles. Pressed by Mr. Stuber, Netflix unveiled a third release model in October, making “Roma” and two other prestige movies available in cinemas first — but only for one to three weeks — and on its service second. Most theaters have refused to comply, although Netflix has cobbled together about 140 theaters in North America for “Roma” and nearly 600 more overseas. (The other two films are “The Ballad of Buster Scruggs,” directed by Joel and Ethan Coen, which only played in 21 domestic theaters last month; and “Bird Box,” a thriller starring Ms. Bullock, that arrived in four theaters on Thursday.)