You have to put it into context, it was the fist multi-user system for most people. Before that, they considered the whole filesystem to be theirs, no pesky permissions or anything like that. So "My" is a good indication for where to put their stuff (instead of, say, C:\).
I think it makes more sense than "Your" as "Your" is more like "stuff the computer gives you / read only" rather than "stuff you give the computer / editable" and a folder like "My Photos" is more of the latter. Matching the idea of the article where "your" is the question, a question is not something you change, and "my" is the answer, which is the thing you act on.
And by the way, the more I look at it, the more I respect the UI designers at pre-Windows 8 Microsoft. So many stupid things that turned out not to be stupid at all. It doesn't mean perfect, but when we see the mess that we have now, it pretty much was by comparison.
Another one is why have folders with spaces in them: "Program Files", "My Documents", etc... The rumor is that it was to force programmers to take handle spaces in filenames properly, because if they don't, it won't work at all. And seeing how terrible the situation is with Unix shells, if true, it is definitely justified. Most of the shell scripts (and not just shell scripts) I see outside of popular public projects fail to handle spaces properly, sometimes catastrophically.