The thing about Antarctica is that it is a continent. The ice is piled on top of it, several miles deep in some places. Above sea level. If that ice were to melt somehow, sea level could rise somewhat. How much is probably mathematically predictable. It would still take a really long time because the sheer mass of it is incomprehensible, and the temperatures there are so far below freezing that a whole lot of warming would have to take place before it even got as high as freezing. That would mean no melting would occur for quite a while.
As to the premise of the article: It is no surprise that water would be found under ice. If there is any geothermal activity in Antarctica, some ice would melt, and since water is heavier than ice, it would stay down there. Ice is also a great insulator. It is quite possible that there are whole lakes and rivers underneath the ice cap. I would bet that bodies of water as big as Lake Tahoe could be found under the ice, in liquid form. With fish.
Even without geothermal activity, the sheer pressure of a mile deep ice sheet would keep the bottom portion in a liquid state. This is nothing new. See Lake Vostok.