No you don’t need information on whether the each guess is right. (And, of course, if the group is playing it correctly, every guess except possible the first one is correct.)
You’re of course right about this not being encoding ‘9 bits of information in 1 bit’. That would be impossible; to encode 9 (arbitrary) bits of information, you need 9 bits.
On the other hand, you must encode information on the colour of 9 hats, and only the last person in the line is free to provide some information. He can’t possibly know the colour of his own hat, so he can only guess – or use his turn to provide 1 bit of information to the rest of the group (while the other people have to shout out their correct hat colour). The difficulty lies in figuring out why the puzzle as stated does not need you to encode 9 bits using 1 bit …
