A bit of follow-up analysis on this:
It was a good catch in the moment, although not quite uh-mazing, in that it's not as though he picked it right off his shoe-tops, or off the ground. He caught it about a foot and a half off the ground. Did he have to actually slide, like into a base, to catch it? Maybe he did. Speaking only for myself, as an outfielder, I find it easier to slide into a catch low off the ground, versus diving forward for it. I feel like I have better control of the process that way. Maybe he does, too?
I saw in an article that the catch he made—based on where Nick started from, how the ball was hit (EV/LA), and where it landed (distance, placement)—had a 65% probability of being caught by a typical big league right fielder. That means the ball should be caught more often than not caught. I'm guessing Nick got his characteristically poor jump on the ball, seeing how the jump portion of his Savant card is so darkly blue. I could not find any video of him just as the ball was hit, i.e., what kind of jump he actually got. But I would think that a player who gets a good jump, or maybe even an average jump, catches that ball without having to catch a grass stain along with it.
Nevertheless, let's give Old Nick his due. Regardless of any of the underlying factors involved, he did catch the ball to extend the game into extra innings, and it was a five-star catch for him. Had he clanked it, the Phillies would have lost on that very play, and Nick would be a temporary goat rather than the temporary GOAT.