A mat is important. But what is more important is good shoes (like oldschool solid heel) or being barefoot. As the article says, the trick is not to be standing all day, but to have that option and mix it up a bit. I stand about 40% of the day, then take my laptop to a couch or other empty desk in the office.
You seem to suggest an anti-fatigue mat was really important - this true? Did you try without it? What happened?