Why is the grammatical structure of "What keeps him going?" right? I got a bit confused over this, when I realized that this structure fundamentally contradicts the basic rule I teach my students: "Questions in the simple present always include do or does (if there's no other auxiliary verb), if they don't start with who".
The ‘rule’ with Wh-questions is a bit more complicated than that.
If a fronted Wh-word represents the subject of the question, neither inversion nor Do-support is required.
Who is the man with the shovel? <<< Bob is the man with the shovel.
What keeps him going? <<< Whisky keeps him going.
If a fronted Wh-word does not represent the subject of the question, then inversion—flipping the subject and the finite verb in the verb chain—is required.
What is he digging? <<< He is digging a ditch.
Why is he digging it? <<< He is digging it to earn enough money to buy a bottle of whisky.
In Present-Day English, only auxiliaries and the verb BE tolerate inversion. If the finite verb is not one of these, then DO-support is required, to supply an auxiliary.
What ✲drinks he? <<< He drinks Jim Beam.
This requires DO-support:
What does he drink?
Rule 3 only started evolving some four hundred years ago, and there are still exceptions to it. For instance, it’s still possible to hear lexical have inverted without DO-support: “What have you in that bag?”
There are moreover questions in which the WH-word is not fronted: “You said what?!” or Bill Franke’s “Sez who?”
But those three ‘baby rules’ should suffice for common-or-garden-variety questions until your students are more knowledgeable.
✲ marks an utterance as unacceptable
You should consider that 'keeps' is acting as an auxiliary verb in this sentence and is being used to form the present progressive tense in place of the verb 'to be,' so "What keeps him going" has the correct structure for a progressive tense question. I can't think of any other examples of this kind of substitution in the progressive tense, but we can replace 'to be' in stative structures e.g., 'That sounds good.'