Diane Zimmerman, an intellectual property professor at the New York University School of Law, said Gawker appeared to be within the copyright law’s “fair use” provision, which permits excerpting copyrighted material for news gathering or criticism.

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The Church of Scientology, founded by the science fiction writer L. Ron Hubbard in the 1950s, also figures prominently in an unauthorized biography of Mr. Cruise by Andrew Morton, which calls Scientology a cult. Published by St. Martin’s Press the same day Gawker posted the video, it was the 25th-best-selling book on Amazon.com on Sunday.

The timing of the imbroglio has been fortunate for Gawker Media. A Gawker editor, Choire Sicha, and two other bloggers resigned last month, and several articles in print publications, including The New York Times, have examined whether Gawker’s relevance and popularity were waning.

But according to the Internet tracker Site Meter, unique visitors to the six-year-old site more than doubled, to more than 13.6 million so far this month, from 6.7 million last January, because of popularity of the posts related to Mr. Cruise and to the actor Heath Ledger.

Some former Gawker bloggers have criticized a new compensation system that on top of a base rate pays $7.50 for every 1,000 views that posts generate. If one of Mr. Denton’s bloggers had posted the Tom Cruise video, his or her haul thus far would be more than $17,000.