It should be broken into two sentences

Original: "No union victory is bigger than the first win in the United States at Amazon, which many union leaders regard as an existential threat to labor standards across the economy because it touches so many industries and frequently dominates them."

Sentence 1: No union victory is bigger than the first win in the United States at Amazon.

Sentence 2: Many union leaders regard Amazon as an existential threat to labor standards across the economy because it touches so many industries and frequently dominates them.

https://academicguides.waldenu.edu/writingcenter/grammar/run...

"Run-on" has an actual textbook definition. This sentence is very long and clunky, and should probably be broken into two sentences for readability, but it's not a run-on.

To illustrate, this would be a run-on:

No union victory is bigger than the first win in the United States at Amazon, many union leaders regard Amazon as an existential threat to labor standards across the economy because it touches so many industries and frequently dominates them.

Pretty sure OP is confused by the concept of "first win" being the object of the first clause. It feels clunky if you don't read your English like you would read algebra.

It's definitely not. People have just gotten used to very short and simple sentences, these days. Some would call a high percentage of all sentences written before, I dunno, 1970, run-on sentences, plus a good deal of the writing in contemporary but non-general-audience publications.

It's not a run-on, which by definition has two or more independent clauses in the same sentence that are not separated by either (1) punctuation such as a semicolon, colon, or em dash, or (2) a comma plus a coordinating conjunction. The first clause is independent (i.e. it can stand alone as a complete sentence), while the second clause is relative.

Then you'd do great writing for the Times.