First, Shaq admitted on Reddick’s pod that he says stuff just to say it, and he doesn’t owe the listeners honesty, which is a position I find repulsive. I believe though he believes this, and he is just wrong.
Second, Gobert certainly puts in more effort guarding perimeter players that Shaq ever did, and often to great success. Obviously Gobert is elite under the rim, but here’s a collection of all the plays in the playoffs where Gobert was isolated on some of the NBA’s very best wing scorers. This isn’t highlights - it’s every play, 6-for-21.