I think that the chair does appear to have slats in it, and the rope is threaded around them down near where his wrists are secured.
Though in support of the "secretly liking it" argument, if there aren't slats it's presumably for the same reason he doesn't just work the gag free as it's only over his mouth.
Or else, "Shhhhhh, don't spoil it for everyone and just enjoy the nice tied-up acrobat"