In short, it was another a masterful performance in a crucial situation which should make everyone here in Vancouver feel better about it’s beloved team’s goaltending.
I'll put aside for now the matter of using "which" to begin a restrictive clause (feel free to re-visit my tipsy thoughts on that here); the trickier question here arises from that little "it's." A couple of message board commenters jumped on Gallagher for using the contraction for "it is" when clearly the possessive, apostrophe-less, model was called for--hockey fans are notorious sticklers for correct usage, after all.
But I submit that neither one is the correct choice here. It all comes down to arranging the right marriage of pronoun and antecedent, and, in this case, to paraphrase Bill Clinton, it depends on what the definition of "its" is. I'm sure that Gallagher, in his post-game haste, just went with the pronoun that best matched the nearest preceding noun: "Vancouver." But the antecedent in that sentence is not "Vancouver," it is "everyone here in Vancouver." Just try reading it as "make everyone here feel better about its team" and the issue becomes clear. "Everyone" isn't an "it." The pronoun to use in this situation is "their."
Or is it? Some people with pinched faces who wear sweater vests will insist that "everyone" is a singular noun, and because you can't say "everyone are..." you also shouldn't use the plural "their"with it. But I think, this is a rule worth breaking.
In the end, the best way to resolve this whole mess, especially since it's New Year's Eve and we all have drinking to get to, is to recast the phrase thusly: "...make people here in Vancouver feel better about their beloved team's goaltending." There. As is so often the case with even the most vexing issues in life, the best course of action is to find the easiest way to avoid dealing with the problem.