It seems pretty clear from reading the article that Minnesota isn't stopping anybody from taking online courses.
But to be officially recognized in Minnesota requires that the entity providing the education is registered as an educational entity in Minnesota. I'm pretty sure most states have laws like this. Here's why: I know nothing about biology, but without laws like this, there would be nothing stopping me from offering classes on biology.
In this case it's obvious Coursera is legit, but in a lot of cases it may not be so obvious.