The article argues that Martin's time period is actually early modern, with its large cities, banks, multiple religions, and international trade. "A world that actually reflected daily life in the High Middle Ages (12th-century Europe) would be one without large cities or global networks. A diversity of religions would be inconceivable. Many aristocrats wouldn’t be able to read, let alone maintain large libraries. And no one would even know about the continents across the ocean."
By that criteria, an awful lot of "medieval" fantasy isn't medieval at all, since in these days of globalisation it's difficult to conceive of a fantasy world as insular as the above quotation implies. I grew up reading David Eddings' series The Elenium, The Belgariad, and their sequels, and even when they contained armoured knights and the other trappings of chivalry, they also contained the same large libraries and global awareness.
I don't think it really matters if "medieval fantasy" is really medieval. Really that's just a label to stick on part of the speculative fiction genre, like steampunk, or high fantasy, or grimdark. All it means is "fantasy set in a white-dominated land that's a bit like olden-day Europe". What matters is when the label is used to justify anti-social content that some readers object to. The article also points out that "When the series is criticized for its violence, treatment of women, or willingness to ice beloved characters, rejoinders from Martin and his defenders often amount to “that’s just what life was like in the Middle Ages.”"
Except, of course, that it's not how life was in the Middle Ages - see above. It seems laughable to use historical accuracy to counter criticism when you're not actually being historically accurate. Also, I don't believe that - unless you're writing alternative history - you should be claiming accuracy while including things like decades-long winters, walking dead, or dragons. You're either writing fantasy or not.
So by all means, don't make your fantasy accurately medieval - but don't then tell readers it is and expect them to stomach the unpleasant things you crowbar in in the name of accuracy.