It's basically a tour of old hyperlink and windowing systems... with lots of guessing and maybes. I'm not sure why it's relevant that Win 3.1 had blue titlebars, for instance. The author never actually answers her question but I imagine the obvious guess is the correct one:
Black text on a white background was the predominant GUI style at the time (probably due to Mac OS and Windows) and the software designers needed a visual cue that the hyperlink was clickable. Just underlined wouldn't have worked because underline was already a popular style in text processing. So they decided to give it a different color too. Blue is the most logical choice as it has good contrast against a white background, and has a neutral meaning (compared to say, red). There weren't really a lot of color choices back then, the largest palette you could count on at the time was 16 colors.
This was what Mosaic did and most browsers that came after it (including the most influential: Netscape) did what Mosaic did.
And there certainly were browsers of the era that didn't use blue underline for links, the next most common paradigm was some kind of bordered box around the text (usually the same color as the text).