it's not "underwater ice", it's "ice sitting on soil that is below sea level". The ice sheet is thick enough to be significantly above water level, but it's especially vulnerable to temperature increases in the ocean, since ocean water can start flowing under the ice and melt it from below.
The article is about ice on land melting. But actually when floating ice melts it increases sea levels a little bit as well, as explained here: https://www.quora.com/If-water-is-denser-than-ice-why-do-sea...
Note, especially the first answer, which says that the effect from melting floating ice is quite small and that the primary drivers of rising sea levels from global warming are melting ice on land and thermal expansion of sea water.
It's not the only flaw in the article. Also it chooses to ignore the fact that unlike the Arctic, the Antartic does actually not have any net ice loss at all; in some parts the ice is melting, but this loss is offset by other parts which are gaining in volume.
> when land ice melts and flows into the oceans global sea levels rise on average; when sea ice melts sea levels do not change measurably but other parts of the climate system are affected, like increased absorbtion of solar energy by the darker oceans.
> Basically Antartica has been losing land ice while sea ice has been growing.
The Nasa article says the reverse, land ice is growing and sea ice melting. Also the NYT article states that it is especially the Antarctic sea ice that is vulnerable because of the rising ocean water temperature.
But I've read your link and learned that the Nasa article is controversial. Well what do I know ..