ESPN tried to educate fans about the game doesn't work.
Who cares about the rules break it down and make it very simple. To win you have to outscore the other team. To score your team has to get the puck in the opposing net more times than the opposition scores on your team.
Very simple.
What works is getting fans into the arenas. More promotions with the AHL, ECHL, CHL, UHL, USJHL, whatever freaking league is out there needs to be promoted. For the most part NHL teams are not in direct competition with these leagues.
Once people attend a hockey game the game itself can do the job. I've seen it happen here in Texas.
Also, more promotions to get fans from within a 3-4 hour radius of NHL cities to games. Package deals with hotels and restaurants, etc.
Once people find out they enjoy the games they will watch on TV. This increases TV revenue.
Marketing is all about getting people to try your product. Once they are there it is up to the League, teams, players, coaches, arena staff, etc. to work together and share ideas to make the product live up to expectations.
The biggest problem in the NHL is not doing more to get people to all the games on a league wide basis and sharing ideas and know-how will definitely make the job easier and more effective.