suh LAH nee (answer)
nih tee MAK ee (answer)
NEE nuh muh (answer)
huh LEHN ee uhz (answer)
These are 2002 examples, but I assure you, the quality of the product hasn't changed one bit. My Russian isn't nearly good enough to comment, except to say that my guesses have been better than the NHL's, but here's a Swedish example:
SHOH struhm (answer)
Yeah, you probably guessed that one, but seriously, even surly Finnish teenagers flunking compulsory Swedish class know better than that.
For any readers who don't speak Finnish or Swedish, take my word for it: the people behind that "pronounciation guide" don't have the faintest idea what they're doing. But it's not just that the league and the broadcasters don't know how to pronounce European names, it's that they're deliberately disseminating, almost mandating, the incorrect pronounciation of those names. In the information age, frankly, it's offensive. It cannot be beyond the league and the broadcasters to find out how players' names are actually pronounced. That they refuse to do so is, quite simply, racist.
There is, of course, a political side to this. The most notable exponent of mispronounciation is, unsurprisingly, Don Cherry, whose renditions of European names are, well, wrong. He's admitted to doing it on purpose, because he's a racist. That isn't surprising, but it was a little surprising to read this tweet from Adam Proteau of the Hockey News, one of the more liberal voices in hockey:
So remember this: according to Proteau, pronouncing foreign names correctly is racist. I have to admit, I don't even know what to say to that. On reflection, I suppose it shows how deeply internalized the racism is. Even to a liberal commentator who regularly calls out Cherry and his ilk for their racist and misogynistic nonsense, the notion of finding out how to pronounce a foreign name is so repulsive that he creates a convoluted, MRA-esque pseudo-logic that makes respecting a foreign language racist. I don't think I'm going to be able to read his columns the same way again.
We, at least, can try to be constructive about this. To avoid being racist against our North American friends, I suggest that if Finnish readers want to refer to the creator of the NHL "pronounciation" guide, broadcaster Mike Emrich, they pronounce his name miik umrääk. Be sure to respect hockey journalism and avoid racism by carefully enunciating Adam Proteau as älän prötöö, and Don Cherry's robustly Canadian name is correctly pronounced reimond luksuri jätst. Remember: they would want you to say it like that. Because the "correct" way would be racist.