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.
Many of the suttas show the Buddha asking "leading questions", 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 think I found this line of questioning persuasive when I read it for the first time (though I wasn't always convinced by Socrates' for what that's worth). I'm not sure why the technique can be helpful, perhaps it lets the student experience working something out for themself.
As an aside, I wonder if the technique helps to bypass a student's resistance to dogma. If you made a claim like, "Greed is harmful!", then I might question that, "Oh yeah? Isn't that what makes people work for a living? Don't people say that's the best way to organise society?" Or saying "Greed is harmful!" would be saying that greed is always harmful (and I wonder whether that's true), whereas when the student answers they're admitting that it's generally harmful -- also the question supplies a little more context, e.g. that it's about what's "arising".
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?"
I think that one is (again) a question about doctrine, but this one is a bit practical too: i.e. "So there's some doctrine, more- or less-well learned ... can you practice it?"
When I learned Maths, for what it's worth, the lessons were half theory and half practice: the teacher would explain some theory or a new technique, and the second half of the class was student exercises in applying that technique to some problem.
I think that not all of the Zen stories are so obviously connected to a specific piece of of Dhamma (at least, that I recognise as such), e.g. there is some obvious "moral" to the story (or several orals) of Is That So? but the protagonist isn't so obviously asking a Dhamma question.