I'd be careful drawing broad conclusions from that study given the data source (https://www.gwern.net/docs/sociology/2016-fales.pdf): The bulk of the sample data came from an NBC News online poll. Online polls are subject to known biases (https://www.pewresearch.org/methods/2020/02/18/assessing-the...).

The second study (with a smaller but believed to be more representative sample) asked slightly different questions, and concluded that there was some statistical significance on "Makes at least as much money as I do" and "Has a successful career," which don't by themselves support the hypothesis that "women by and large prefer men to have a higher career title than themselves" (though I can agree that it waggles its eyebrows and points in that direction; perhaps suggesting follow-up studies).