Well, the Greeks calculated the circumference of the earth long before. Several of their other things are also not correct -- the 'pinhole' camera was known by the Greeks (who described its reversing behaviour as well as using it to view a solar eclipse) and the word camera comes from the Latin for a room earlier than the Arabic (we may have got it via Arabic for the specific "camera obscura" but that isn't certain, because phrases like "in camera" meaning "in chambers rather than out in the open court come from Latin). They admit that chess originated in India, but elide the Persian and Muslim connections (it was the Arabic conquerers of Persia -- which wasn't Muslim -- who then spread it to Europe). Windmills, too, were known in Greece and Persia (Afghanistan).

I don't know how much the journalist is "dumbing it down" (I can't find any references for his list via the linked site), but to me it reads rather like the list of 'Turkish' influences on Britain which were expounded by the Prophet of the Moon Misysra Ammon in G.K. Chesterton's "The Flying Inn" in an attempt to turn Britain Islamic. Which is a pity, because the way that so many of the things did indeed come to us via the Arabic world is informative, they just weren't necessarily the first. I hope that the actual museum descriptions are more accurate.