The article points that out. "Destabilization" (my term) refers to what the article describes as increased melting leading to accelerated disintegration; major sea-level rise isn't necessary to initiate large-scale disintegration. Note that the article points out that the process is expected to be non-linear (meaning hard to predict), and that once "large-scale" break up starts it will be virtually impossible to stop.
A lot of ice sheets are prevented from faster flow to the ocean by the ice tongue or outflow area that is anchored to the bottom. If this area becomes disconnected from the bottom, ice sheet flows can accelerate.
The only quantitative study I can find is about ice sheets in Antarctica accelerating when the locking ice shelves broke up. I haven't found anything on polar ice sheets breaking up, only non-polar. With the snow increasing in Greenland and Antarctica, it's hard to imagine a break-up from "disintegration".