Yes, there is a gender wage gap. Yes, some fraction (maybe a lot maybe very little) is due to discrimination. No, I don't think people should harp on the numbers because the statistics in this case are just not very good, and Bryce is a bit misleading in the numbers she casually tosses out in the above linked piece.
The best numbers available are probably from Gov Accountability Office (GAO), where they make a major effort to factor out life choices, and that effort cuts the pay gap by more than 50% (the report covers 1983 - 2000 so you can't compare those results directly to the current gap as she did) so the 21% gap that results is compared to a 44% uncorrected gap, which is much larger than the current 23% gap and could imply that the corrected gap today is anywhere from ~20% to less than 5% to anything between. The infuriating thing is the numbers/statistics squabbling. The issue of fair pay should be an easy one for everyone to get behind. If discrimination is a huge issue then enacting laws that counter that is necessary and will do good things for women and families. If discrimination is a complete non-issue, then enacting laws preventing discrimination will lead to no improvement because there is nothing to fix.
Just pass and enact the damned laws! If the pay gap shrinks, we'll know it works, if it doesn't we will know that there is more going on and we will have information on where to look next.