Interesting. I must admit I know very little about zonal defense in hockey. Tried to find something on the web, but mostly is was about the starting positions in the system. How does this system work when the first defender fail? Is it the nearest guy who then goes to work? Reason I ask is that in the early nineties Norway got a new coach for the national soccer team. With a strict zonal defense he took the team from nowhere to 2nd in the FIFA World ranking. When he described how it worked I found it was much more complex than players defending their zone. Very very very simplified the nearest defender would defend against the player who had the ball and rest would position themselves according to that. So the next guy could try if the first defender failed.
There's really 3 "schemes" in the NHL. Zone, Man on Man, and Box+1. All of the schemes have switches in coverage, but it's how you switch, and where you are on the ice that limits passing lanes. The success of each depends on the overall style of play, and personnel that you have. Most teams either do a zone or a man on man. Some teams will still deploy a box+1, but you need good centers with young legs in today's game to play that effectively, otherwise you where your guys out.
I'm a bit short on time, so I'll cover zone for now, and post the rest later.
Zone:
The CLB Bluejackets are one of the better zone defense teams out there. The same was true for the 2012 Rangers. Tortorella preaches this system, but you need the right personnel for it. A good zone defense will contain teams on the outside, take away the cross ice pass, and hardly ever have a defenseman vacate the slot without a coverage switch. There are more stops and starts.
If you have a defense that's willing to block shots, especially after a cross pass, then this helps the goalie out tremendously. Teams like Vegas, the 2016 Panthers, the Trotz teams are won or are winning with older or "weaker" goaltenders because the team structure is designed to prevent shots and one-timers from "in-the-box".
The "box" is the homeplate shape from the top side of each crease to the faceoff dots, and the area in front. Outside of Stamkos and Ovechkin, there are not a lot of guys who can consistently beat a goalie clean outside the box, and even then that's on the PP. Most NHL goalies can stop shots outside the box, especially from a non-rush situation.
Teams that play zone effectively will take a trade-off of pressuring aggressively, and actually give-away end zone time if the puck and passing options are kept outside the box. This is one of those things that shows poorly in some corsi stats or timed possession stats, and I've heard about luck and regression towards the mean on this phenomena, but always found it to be dumb because you have teams that do this by design, and do it very well. The Trotz teams are probably the best at this in the current NHL but they are one of the worst "timed possession teams".
If the Rangers are trying to play a zone, then they are doing it poorly. In a zone scheme, it's a cardinal sin to have both defense below the red line, or vacate coverage in the box to pressure the puck carrier, unless the center switches. This also requires the wingers to collapse and provide support. A good offensive team will try to counter this by either bringing a 5 man forecheck, or throwing it back to the point. A point shot that's well outside the box is the trade off. If the forwards are willing to block that shot, then you take away the danger of a scoring chance. Not counting bad bounces.