The only one of the car-free islands they list that I have been to is Sark, but they did not list another car free island I have visited which I found even more appealing, That is Buyukada in the Princes Islands in the Sea of Marmara off of Istanbul.
Buyukada and the Princes Islands generally was the first place that the Ottoman Empire allowed foreign citizens to own land and that was only in the mid 19th century. From that time until World War I, there were many fine mansions built there by foreign merchants and diplomats, as well as Ottoman aristocrats, after which development came to a crawl. It is a wonderfully atmospheric place, and travel around the island is by horse and carriage, which are fairly reasonably priced. There are regular ferries multiple times a day to the Golden Horn in Istanbul. I would certainly have put Buyukada on the list in that article.
Sark was also an interesting place, the last feudal state in the world. It was a feudal dependency of the Duchy of Normandy when William the Conquer invaded England, but when France later took over Normandy, the feudal ruling family whose title is "siegneur" kept their allegiance to the British crown. They are under the British king but not the British parliament. The seigneur was absolute ruler until in the late 20th century he delegated some authority to an elected body on the island. While cars are banned from a decree by an early 20th century seigneur, they do allow tractors and most transport on the island involves a tractor pulling some type of trailer that people ride in.