Correct. No one else joined him in his concurrence and that is significant. If 5 or more Justices agreed with what he said, he would have written the majority opinion and what he wrote would have been the law of the land. Because that didn't happen, what Kavanaugh wrote isn't binding precedent. It is what is called "dicta." If any of less than 5 agreed with him, they could have and would have joined him in his concurrence. None did, meaning they don't agree with what he said. It's not unusual for more than one person to join a concurrence, or to have more than one concurrence. Sometimes cases will have 4 or 5 opinions ... the majority, the dissent, and then multiple concurrences to both the majority and dissenting opinions. In a 5 to 4 decision, you might get the majority with 2 concurrences explaining how they would have gone further, and then the dissent where you might have 2 groups of 2 who give two different reasons for why they dissent.
It's one of the frustrating things I see when sports writers and others quote Kavanaugh's concurrence as if it is binding law. It's not. That's not to say what he wrote isn't important. Justices often write concurrences to provide future litigants with a framework as to how they might challenge the issue further. But again, he would have to convince at least 4 other Justices to go along with his broader interpretation for that to become the law.
If you listen to the oral arguments you see why they didn't join him. Most of the other Justices made it clear they see this as a very unique area, and they are very deferential to college athletes and the difference between college and pro sports. Even Kavanaugh acknowledges that, he just thinks it shouldn't matter. His is a throw the baby out with the bath water view, while the others are more cautious.
I got curious to see if I could find the SCOTUS case with the most opinions. I didn't, but I did find a quick quote that wraps up what I was saying:
Once the votes have been tallied, the senior justice in the majority (either the chief justice or, if he dissents, the justice in the majority who has served on the court the longest) will assign someone to write the majority opinion.
If a minority of justices believe that the case should have reached a different outcome, the senior most justice in that group assigns someone to write a dissenting opinion. Any justice can also write a separate dissent of their own.
And if a justice agrees with the decision but disagrees with the reasoning behind it, they may write a concurring opinion, which others have the option to join.
The thing I got wrong is that you don't have concurrences to the dissent. You have multiple dissents, although that seems to be a matter of form over substance.
Hope that clears up the confusion.