It looks like the total amount of estimated ice in Antarctica is something like 30,000,000 cubic kilometers, give or take. In comparison, the amount of ice being lost here probably doesn't even amount to rounding error; it's more like just noise. (Someone else here has calculated a value of about 0.01%, but I don't know how accurate that is.)

That's a common theme with such reports these days, BTW. The numbers quoted can be scary at first, but looking at the bigger picture they often turn out to fall into the margin-of-error/statistical-noise range - a bit disconcerting, maybe, but not something to get too worked up about.

What's more interesting to me is usually what's left out of such reports. For example, there are claims that while ice may be melting around the edges of Antarctica (at least in certain parts of it), a lot of that may just end back up as snow in the interior instead of actually staying in the ocean. And while "warming waters" might be caused by climate change, they might also be due to geothermal activity in and around Antarctica - undersea thermal vents and such. The continent itself should have about the same level of volcanic and geothermal activity that any other continent typically has, which of course ebbs and flows, but it's generally hidden from view under all that ice.

A poor estimate is that 1 trillion tones of ice is 1000 cubic kilometers.