I have ESPN + on my Apple TV.
They show complete "regular season" games during the regular season. I'm not so sure, but the one time I looked for playoff games on ESPN +, I didn't see any games. I've been watching the playoff games on cable since then.
ESPN + was working fine on Apple TV. NHLTV.com is no longer offered in United States since ESPN won the broadcasting rights. Maybe you live outside of the U.S. or something?
One thing I don't like on Apple TV is their menu system. It takes too long to find the NHL game you want to watch (too many steps). You should just be able to select NHL games, and then pick the game using a table/text (that was the way NHLTV.com did it). Also, if they had a calendar function for past games, it would be great and more useful so that you could select games that have already been played that you missed. Again, I'd simply & reduce the number of steps and use a less graphical (drop the pictures) user interface.