What kind of model is used by 20 Questions?
You just play once with it, observe it, and you have the model. Try
something non obvious, or simply cheat with answers.

The game: you think of something, and 20Q asks questions to find what
it is.

They just collect the answers from the players.  They have a
collection of questions that are supposed to discriminate solutions.
They ask questions to users, who chooses among 7 possible answers. Recall that with just 20 yes/no answers, you can discriminate 1 million different objects. And their questions have more answers that just two.
The combinatorics of the answers will identify the right "something"to
be guessed in the available collection. If the thing they are supposed
to identify has not appeared before, they do not find it, recognize
that they lost, ans ask what it is.  Then it goes into the database,
with all the user's answers to identify it the next time.

So they fail, but not twice on the same "something/someone/somewhere"
to be guessed.  Unless users give wrong answers to questions (the
first time, or afterwards ...?).

It is probably slightly subtler, but I doubt it has much artificial
intelligence, neural network or otherwise.  A most elementary and
simplistic form of machine learning, if one dares use the expression
for it.

This is all pure guesswork from what I observed. No idea where you
could read about it. Not sure there is anything worth reading anyway.