I think he means the demographics of the court. Being 6-3 conservative from 5-4 liberal from only a few years ago is quite a shift.
Yes.
Is this something the Supreme Court could enforce on their own or would they need Congress' approval?
The supreme court basically did this (legalized gay marriage) on their own the first time around. They got a good case, and ruled that laws restricting marriage to man and woman are unconstitutional (either through the establishment clause or equal protection, I haven't read Obergefell). The supremes are basically asking people to bring a similar case now that they have more conservatives, so that they can overturn Obergefell. Or at least they were, not sure they're doing that now that the democrats have the executive and congress. I think they might be quiet for a while hoping they can wait less of a legislative mandate in the other branches before they start shaking things up.
They could overturn Obergefell on their own. No need for congressional approval. Just like Roe v. Wade (legalized abortion).
And just like roe v. wade, there are a variety of potential stances that the court could take. Right now, for both Obergefell and Roe v. Wade, the court's opinion is that states cannot restrict any further than they have. Meaning states are now allowed to restrict it. But there are two other positions that the court could take - that it can be restricted, or that it
has to be restricted. The middle ground could be potentially circumvented by federal legislation. So congress and the executive can work together to pass legislation for gay marriage and abortion that tries to prevent its restriction if the supreme court says it can be restricted. In other words, the federal government can try to step in and say "just because the constitution says this is ok, doesn't mean we do". That could be tricky, because the supreme court could rule that congress can't do that, it has to be done at the state level. It's worth noting that the federal government does this for marijuana right now. It's constitutional, but not federally legal. But if the supreme court were to say it
has to be restricted, congress and the executive can't do anything about it except pack the court.
So for example, if a supreme court ruling said that "defining marriage as anything other than a man and a woman violates the establishment clause" - in otherwords, marriage is constitutionally enshrined as heterosexual - then there is no recourse. And that appears to be what at least Thomas and Alito are arguing. Similarly they can establish abortion in all forms as being murder, and thus not permissible according to the constitution (I don't know what the technical argument would be... due process?). The federal and state governments could do nothing to stop that. This would be akin to making permission of abortion or gay marriage similar to gun control laws - constitutionally prevented (to a degree) at all levels.
We really do have a problem at the supreme court. It has been quiet for a little while, but it's still there.