Here's my take on the whole situation:
1. The ruling, if upheld, only applies to private institutions because the NLRA only applies to private employers. For public institutions, it would be a state by state determination, and given the differences from state to state in terms of labor issues, you would wind up with some states classifying athletes as employees and some states not doing so. For example, Florida ( which is a right to work state with no unions) would not allow its college athletes to unionize while all the athletes in California (which allows unions) could do so. Basically, this would be an impossible system to allow college sports to continue.
2. The tax issues have a huge impact and I don't know where to begin. As of now, no taxes are paid by universities related to benefits provided student athletes. That would go away, because this is compensation for employees, which means it is taxable. Athletic departments would also lose their tax exempt status, meaning that any revenue earned would be taxed AND meaning that alumni/booster donations would be taxed as well. The money that boosters pay to the program to get better season tickets now becomes taxable revenue for the school AND it is no longer a tax deduction for the booster because they aren't donating to a tax-exempt organization. Imagine what that could do to the amounts collected from alumni/season ticket holders? All these huge donations, like Stephen Ross to Michigan would just go away. Bowl games/organizations are also tax exempt, and that would go away as well. Consider the number of athletic departments that break even and struggle to end the year with any left over revenue. Now they have Uncle Sam taking a big bite out that revenue. Additionally, if you are an employee, and you are receiving an economic benefit from your employer, you have to pay taxes on that benefit received. Therefore, the value of an athlete's scholarship could be taxed as well.
The only way unionization isn't a death blow to college athletics is if instead this is simply an impetus to getting changes to the system and we end up with no unions, but a re-designed system, including things like full cost of attendance, additional health benefits, etc.
Realize, that even a change that provides some portion of revenue to the players related to names/likenesses could possibly have huge tax ramifications. The article below explains it all.
http://thefederalist.com/2014/02/03/dont-expect-college-athletes-to-unionize-any-time-soon/