The ocean freezing anywhere is irrelevant: the mass of water in the ocean stays the same regardless of its phase.
The problem discussed here is the Greenlad ice cap melting, which we can assume increases the mass of water in the ocean.
The nature of ice caps in both Greenland and Antarctica is that they are in deserts that go for years with zero precipitation. Ice accumulates steadily through what we can think of as layers of frost every morning over centuries until it covers entire continents kilometers deep. On the other hand, surface melt due to increased seasonal insolation usually doesn't result in much runoff: these are not glaciers that slowly flow out to sea, either.
Just to make sure the context is clear, my main question is why the article headline says this particular melt caused a 2.2mm global rise in sea level. The melting described in the article would only account for a 1.8mm rise, in isolation. If anything happening in Antarctica had an effect, it would lower that number even further, making it more different from the headline. Does the 2.2mm number include other melting that the article and cited paper don't mention?
The problem discussed here is the Greenlad ice cap melting, which we can assume increases the mass of water in the ocean.
The nature of ice caps in both Greenland and Antarctica is that they are in deserts that go for years with zero precipitation. Ice accumulates steadily through what we can think of as layers of frost every morning over centuries until it covers entire continents kilometers deep. On the other hand, surface melt due to increased seasonal insolation usually doesn't result in much runoff: these are not glaciers that slowly flow out to sea, either.