I would agree with a poster or two here that this is, in fact, a decent introductory kids joke. Not the FIRST, but a very early one.

Humor relies on the unexpected. This joke is a meta-joke, for sure, but the humor is still (as with other jokes) in the unexpected.

The question, "why did the chicken cross the road?" Is clearly asked in a joking manner. Thus, the "expectation" is a joking answer.

When the answer treats the inquiry as a conventional question, that is unexpected, and thus the source of the humor.

Thus, the only prerequisite for this to be funny is not exposure to reams ofjokes and riddles, it's exposure to just enough of them to set the expectation that this, too, will have a funny answer.