Isn't this a too narrow definition of entopy? Ok. Pure physical entropy was the first and original usage, but now informational entropy can be used at higher level, and it correlates well with disorder at that level.
If I sort an array its entropy will be lower - while due to thermodynamics the total entropy of the world will be increased.
So there is the only the high level component I'm interested in: I see less macrostate in a sorted array(one) than in an undordered(n factorial) even if the microstates in the world have increased(I don't care).
Same goes for the article examples, for me subjectively an ice statue can have many different forms (macrostates), if it melts it will have one form (a puddle) - so I see the entropy to decrease - of course the puddle have more microstates than the ice statue - just I do not differentiate between them...
True: in the sbove examples things became more ordered at high level (entropy have decreased), meanwhile physical entropy have increased - but that increase was global and in our local point of interest it is still can be said (according to modern usage) that entropy have decreased!
Of course the total sum have to be positive - that's the basis of how for example the Landauer principle is calculated, wich connects the above high level informational view with physical entropy...