The Antarctic ice sheet contains 26.5 million cubic kilometres.
Also, just because melting sea ice doesn't directly contribute to rising sea levels, doesn't mean it isn't still a factor. From another NSIDC article, What are the impacts of Arctic sea ice loss?:
Sea ice loss contributes to Arctic amplification
Light-colored surfaces, like sea ice, have high albedo, meaning they reflect most of the sunlight that reaches them. Dark surfaces, like the surrounding ocean water, have low albedo.
At the height of summer, when the Sun shines relentlessly on the Arctic Ocean, exposed ocean water absorbs nine times as much solar radiation, if not more, than sea ice does. Before ice can form again in the fall, the ocean must release the absorbed heat into the atmosphere. The loss of sea ice warms the Arctic, contributing to a phenomenon known as “Arctic amplification” where the Arctic warms at a faster rate than lower latitudes. [...]
Does sea ice loss raise sea levels?
Just as sea ice absorbs wave energy and reduces wave action along shorelines, sea ice reduces wave action on ice, namely ice shelves (thick slabs of ice attached to coastlines that float over the ocean surface) and water-terminating glaciers. Increased wave action caused by sea ice retreat can flex and bend these ice bodies, increasing the possibility of retreat. Glaciers that have lost their ice fronts tend to flow faster, and because this process introduces a body of ice into the ocean that was not there previously, it raises sea level.
For what it's worth, current research indicates that a substantial fraction of Earth's water (and hence of the glacial ice) may be from outer space1 but as I said, it would raise sea levels no more and no less than "domestic" ice.
1 Well, Earth itself is from outer space, so to speak, because it is accumulated interplanetary matter from the accretion disk of the Sun. What the theory says is that the original composition of Earth's material did not have very much water in it because it was too hot for water to condense; and that oxidation of hydrogen over geological time frames does not suffice to produce the amounts we see today. Since many asteroids contain significant amounts of water they are one of the suggested sources for the water on Earth. So the suggestion is that water was added later in Earth's geological history.
Thermal expansion of the ocean is responsible for about half the sea level rise:
First, warmer water expands, and this "thermal expansion" of the ocean has contributed about half of the 2.8 inches (7 centimeters) of global mean sea level rise we've seen over the last 25 years, Nerem said. Second, melting land ice flows into the ocean, also increasing sea level across the globe.
See: https://climate.nasa.gov/news/2680/new-study-finds-sea-level-rise-accelerating/
This however is only one of the reasons that the water level rises. As many others have pointed out, much of the glacier is not floating on water -- they are on land. Their melting and pouring into the ocean would obviously increase the water level. Thermal expansion goes the same direction.