Recommend everyone who is interested read the full decision: https://s3.documentcloud.org/documents/20969583/20-512_gfbh.pdf
In truth, the majority opinion seems not particularly remarkable, nor particularly wide-ranging. They basically rubber-stamped the Ninth Circuit decision and said that the NCAA had no compelling arguments to reverse it.
Beyond that, the final portions of the majority opinion were actually quite deferential to the NCAA. Essentially they didn't say "you can't regulate this", they said "you can't prohibit this, but you can enact regulations and limits to ensure that academic/educational benefits are legitimate and pro-competitive".
Kavanaugh's concurring opinion raises eyebrows, but that's about all it can do legally. While the majority opinion has the force of law, his concurrence does not. And it's telling that no other justices signed on to his concurrence. It's a nothing-burger.