The mechanics are what make the ruling readable. The executive order directs states to hand the Postal Service lists of voters who requested mail ballots, and requires ballot envelopes to carry a barcode [1]. The enforcement is the part that matters: USPS refuses delivery for voters not on the list, or for envelopes without the barcode [1]. A ballot could fail to arrive because of a printing specification.
On July 23, US District Judge Indira Talwani held that this is unconstitutional, and allowed the challenge led by the League of Women Voters to proceed [1].
Her reasoning ran along two lines. The first is the allocation of constitutional power: 'The President plays no role in the regulation of elections' [1]. The second is statutory, and narrower: 'Congress has not delegated authority to USPS to sort the mail, let alone to refuse to transmit mail ballots' [1]. Neither the president nor the Postal Service, on this reading, was given the job the order assigns.
Talwani also found the harm is not hypothetical, writing that disenfranchisement 'as to the upcoming election is plausibly likely and imminent' [1]. She had already blocked implementation in 22 states and the District of Columbia [1].
The case is not over - the next hearing is August 7, and this ruling lets the challenge continue rather than ending the matter [1]. What it settles in the meantime is the simplest answer to the question the order raised: regulating elections is not the president's to do [1].