Be warned, wall of text incoming. 

First, I would like to address your "non-profit" comment. 

The NFL league office is the only part of the NFL that is "non-profit". Revenue from the NFL is distributed to the individual teams through a revenue sharing system that provides more money to teams that are generating less revenue on their own and less money to teams in large markets like NYC.  

This revenue is, indeed, taxed. Every cent. 

Your assumption that the NFL as a whole is tax-exempt is a common one, because people hear that the league office has non-profit status and simply assume the league pays no taxes. The reason the league office has that non-profit status is mostly because of the way the penalizes players for certain infractions and uses said money for charitable purposes. 

But make no mistake, each team pays their fair share of taxes. I am sure each team has ways of finding tax loopholes like any other large business, but they are not tax exempt. 

Now, as far as the benefit to the state. 

It is fairly obvious the most direct benefit to the state is the influx of cash from all the media outlets and football fans from around the world spending almost a week in Minneapolis for the event. 

This creates far more cash for a northern city like Minneapolis, than it would for a city like New Orleans due to the "Substitution effect." In cities like New Orleans, a Super Bowl would actually displace people who would normally be in the city on vacation in February. This means that any revenue generated by the Super Bowl has to be adjusted to account for the people who would normally be there on vacation. 

This is why so many people talk about how the Super Bowl does not bring as much money as you think, primarily due to this substitution effect. But in Minneapolis, there are not a lot of people who are interested in traveling to the city in the first week of February. So the substitution effect is far less substantial. 

In fact, the article that Paul linked that has "Three reasons a Super Bowl might not be worth as much as you think," all three reasons are portions of the substitution effect. 

The next benefit is the taxes from the players. The Super Bowl winners and losers get a bonus check for the games played, which came out to a total of $8.7 million paid to the players that were involved. Those bonus checks are, indeed, taxed as income by the state. 

There is also the TV ad revenue which will be taxed by the state as well, since the event is hosted on their soil. 

You also have to consider the lingering effect of the Super Bowl. It will bring people to the area that wouldn't otherwise visit and that likely will have a cascading effect, causing at least some of the visitors to make return trips if everything goes well. Very difficult to quantify, but certainly a factor. 

Not to mention the sales tax for the tickets. But, here is where it gets a little sticky, since about the 1990s, most Super Bowl host committees have given tax breaks on the sales tax to the NFL, with some states even footing even more of the bill for security and parking. Take New Jersey, for example, they basically paid about 8 million to the NFL for the luxury of hosting the event. 

So the question is, what kind of concessions did the Vikings Super Bowl committee have approved by the state? I have not heard of any, and usually there would be complaints about the concessions given almost immediately after the awarding of the event. This is important information that is currently unavailable. 

To make a long story short, there are benefits and conservative numbers put it in the range of $60-120 million in economic benefit to the state, which is far short of the $600 million that the league likes to trumpet. 

Sure, I might not see a cent of that money living up here in the northwoods. But anything good for the state is ... well ... good for the state. I don't think you can argue that hosting a super bowl is not good for the state.