Some Linux distributions are not free (Red Hat Enterprise Linux for instance).
Also, the free probably refers to free software - free as in beer, and not as in free beer ;)
I know some distros are not free software, but I don't know any.
I think you are mixing up free software and open source software. The vast majority of Linux distributions are not free software. See http://www.gnu.org/distros/free-distros.html. In the context of the article, I'm confident the "free" in the title refers to "free" as in "free beer".
Good point, none of the distributions presented in this article are fully free software. For example, Linux Mint comes with some non-free software media codecs, and the package managers of all these 5 distros allow you to install non-free software like Adobe Flash.