It certainly can't help relations between Russia and NATO. I don't see a direct threat to NATO, nor is any intended I believe, but with Russia claiming as effectively territorial waters beyond the 12 mile teritorial limit and the 200 mile economic limit to include the continental shelf, and therefore, practically half of the Arctic Ocean, such a bold claim and any subsequent efforts to enforce it are going to cause tensions.
Personally, as long as Russia doesn't become aggressive outside of the areas it is laying claim to, I am not seriously concerned, although still somewhat wary. The US will not take this lying down, and I suspect Norway and Denmark will take whatever measures they find they are capable of to preserve their own claims. Canada apparently is going to build a new base at Resolute on Cornwallis Island, in the middle of the North-West Passage, the right place for it, but it appears that it will feature little in the way of a meaningful military presence, probably just a glorified token presence.