You don't understand how basically using shots for and against is not advanced?
If anything it is over-simplistic and basically saying if you take more shots than you allow you will win.
And how do they not measure possession? Possession is possession not shots, possession to be measured has to be measured in time. That is the only way to measure possession. These stats put more value on a handful of lazy shots from the perimeter then they do from a good cycle that results in just 1 shot that is a good scoring chance.
Even their scoring chances are determined by location on the ice and not the actual quality for the scoring chance.
Like Snazu pointed out, advanced stats do not work well for hockey as there are too many variables.