"The right of the president of the United States to withhold information from Congress or the courts."

The article you mentioned cites executive privilege multiple times, and describes how it is unclear what the boundaries are. Simply saying "The House issued a subpoena and therefore the executive branch must comply" is just as invalid as "The executive branch can ignore all subpoenas".

You said you didn't know what the DOJ/Trump administration was standing on to not comply with the congressional subpoenas. I explained they were standing on executive privilege.

As the article you linked described, the Trump administration was asserting executive privilege, and conflicts between congressional demands and executive privilege assertions need to be mediated by the courts ("But each of the emerging fights raises somewhat different legal questions that courts would have to sort through."). When the administration asserted privilege and declined to comply with House demands, the House chose proceed without court rulings, though courts probably would have compelled testimony about information previously revealed in the Mueller investigation.

For more authoritative sources than your NY Times article provides, executive privilege has been recognized in various supreme court decisions, particularly in military and diplomatic issues, even in cases where the court decided the privilege did not cover the material demanded (like U.S. v. Nixon https://supreme.justia.com/cases/federal/us/418/683/#tab-opi...).

Executive privilege began as early as 1792 in George Washington's first term, when he decided he had authority to withhold information demanded by congress. https://www.thoughtco.com/presidential-executive-privilege-3...