I've gotten more impressed with the Rangers by watching them and then watching other teams in these playoffs. The Rangers do things like keep control of the puck in the offensive zone, move the puck around and make the defense and goalie move, and take good shots much better than other teams I've seen.
On defense, they do a nice job of letting Igor see the puck and then clearing the rebounds (at least most of the time). So teams get shots, even ones that might be counted as "high danger" but that just end up hitting Igor in the chest or pads.
Since most of the advanced analytics seem to focus on shots and shot attempts and don't measure shot quality (except by location), they don't favor the Rangers. A "time of possession" type stat might look better from a NYR perspective. Finally, the Rangers' stats probably don't look great against the Caps because they were running out the clock for a few of those games.
Just some thoughts, probably wrong but thought I'd try.