There are these four ways of answering questions. Which four? There are questions that should be answered categorically [straightforwardly yes, no, this, that]. There are questions that should be answered with an analytical (qualified) answer [defining or redefining the terms]. There are questions that should be answered with a counter-question. There are questions that should be put aside. These are the four ways of answering questions.
There are examples of that (type of rhetoric) in other suttas, e.g. (the first one which comes to mind is) the Kalama Sutta
"What do you think, Kalamas? When greed arises in a person, does it arise for welfare or for harm?"
"For harm, lord."
I don't find it especially subtle to read (and I'm not a big fan of Socrates -- e.g. because I'm not naive about doctrine it's obvious what the "right" answers are); but perhaps the technique is helpful sometimes, I'm not sure why, perhaps for the student to experience working something out for themself.
The example you quoted, from Wikipedia, isn't quite like that: that seems to be an example of questioning the student's thesis (or thinking), which assumes that the student has a thesis -- whereas the line of questioning in the Kalama sutta (for example, though iirc the "Socratic" dialog was similar) follows the Buddha's agenda and doctrine (unless the Kalamas' "They leave us absolutely uncertain & in doubt: Which of these venerable brahmans & contemplatives are speaking the truth, and which ones are lying?" is counted as a thesis).
The protagonist-who-asks-questions, and especially the story-which-ends-with-a-question, does seem of a feature of Zen stories -- of Nothing Exists for example ...
Yamaoka Tesshu, as a young student of Zen, visited one master after another. He called upon Dokuon of Shokoku.
Desiring to show his attainment, he said: "The mind, Buddha, and sentient beings, after all, do not exist. The true nature of phenomena is emptiness. There is no realisation, no delusion, no sage, no mediocrity. There is no giving and nothing to be received."
Dokuon, who was smoking quietly, said nothing. Suddenly he whacked Yamaoka with his bamboo pipe. This made the youth quite angry.
"If nothing exists," inquired Dokuon, "where did this anger come from?"