I've had this problem with Godot html projects before and found a solution. on the Itch page go to edit game, and scroll down to the Embed options and enable SharedArrayBuffer support.
I think I've found the problem, Godot Web projects give that error when the user is viewing it though the Game Jam Random Submission feature. doing random submissions right now and seeing a few Godot projects with that same error, but it works fine if I open the game page without using the View Random Submission.