As a geologist, I see huge failings in this story - the one illustration presented does not match the present-day distribution of subduction zones. Either there is more "meat" in the full scientific paper (not referenced) or the story is "wrong".

The concept is well-established that some of the Earth's water is soaked into near surface rocks, and some in cracks in deeper rocks, and some is dragged into the mantle, so the water inventory of the Earth is certainly more than the oceans alone.

How much more? well that's the $64,000 question. But there don't seem to be any sudden changes in the distribution of water, so don't worry about "mantle upwelling", or other such catastrophic notions.