Do the Shafi'is hold that divorce occurs to a non-mahram woman if the divorce is attributed to ownership after the wife's acquisition of ownership, or does it not occur?

The Shafi'is do not consider a divorce to take effect before marriage. So, if someone made a divorce conditional on marrying a specific woman or an unspecified woman, and then married her, the divorce would not take effect, because divorce does not occur before marriage, nor is it constituted before it. The text mentioned in the question does not establish the Shafi'i madhhab; rather, it quotes the statements of those who disagree with them and refutes them.