There are countless long and short passes that beat 2 or 3 players, which is a huge advantage. But it's a highlight reel, you'd expect as much. What's more important is his comfort level. His defenders are more than willing to pass him balls even in tight positions because they're confident he can handle it and get it back to him. Lets him participate and allows the FBs to be a little more up the pitch, trusting the pass will be a good one. The CBs can split properly far and know the pass won't be underhit or overhit. This entire system is built around inviting pressure onto the Keeper and back 4 in order to create space for the midfielders and attackers as they spring forward. You're begging strikers and wingers to close out the keeper and CBs and lob a pass over them to advanced FBs who now have options available in front of them. You want to get the strikers forward and the wingers out onto those FBs so you can pass to an unmarked pivot with acres of space in front of him, etc. You can't play this with a keeper who just taps the ball out to a CB to deal with or one who puts the other players under pressure with poorly weighted or overhit passes. The passing range must be large and the comfort to have players running at him must be very high. Which is on display all day in that video.
In a perfect world, I'd rather Hart be able to do 80% of this than go get Ter Stegen. But I think it's crystal clear why we are linked.