West antarctic ice only minor worry.
Most of the west antarctic ice sheet is below sea level, so if it melts it'll have a minor effect on sea level rise - if it melts only the ice currently above sea level would contribute to the rise and melting of the ice below sea level would cause a slight _decrease_ in overall sea level due to ice being less dense than water.
Added to that, a lot of west antarctica's ice is floating on water anyway, so melting of that won't have any effect on sea levels at all (same as the water level in a glass only changes until ice in it stops touching the bottom)
(minor = 1-2 metres or so. It's all relative)
You can see the sub-sealevel stuff in the video with all the vast areas of green and blue on the west antarctic side - and the fact that the ice is significantly below sea level at the coast explains why warm currents can erode it so easily.
East antarctica melt is a completely different matter. Virtually the entire icemass is on rock which is above sea level. If that all melted there would be massive changes in sea level - but that ice is hemmed in by mountain ranges, so it can't flow to the sea easily and is showing no real signs of large scale melt in any case.
Short term, Greenland ice is more of a worry, especially given that a good freshwater pulse from melt there would probably cripple the gulf stream for a few years, leading to significantly colder tempratures in europe.
One issue which isn't brought up much is that rifting goes hand in hand with vulcanism and the effects of volcanoes erupting through an icecap have already been seen recently. Imagine that on a much larger scale. :)