"Who is watching him?"
The -i ending :)
It's definite conjugation, so there has to be a definite object -- "the man" or "him" or "that person" or something definite.
Even if it's not stated in the sentence, you can understand from the verb conjugation that there is a definite object in the meaning.
It doesn't accept "Ki nézi". I don't know why, It's correct according to a hungarian friend.
So, there is no way of knowing if you are being asked "Who is watching him, or her, or it, or you?
If you're being asked "Ki figyeli?" by someone, you both should know what is being talked about. The child, for instance. Or the cookies in the oven. There usually has a dialogue happened before that states what this is about.
Out of context, like here, it can mean 'him', 'her', or 'it', or the plural 'they'. Hungarian doesn't make a difference of the genders anyway.
It won't be 'you', though, at least not the informal variants of te and ti, since those require the indefinite conjugation to be used: "Ki figyel téged?" - Who is watching you?
I think in those cases it's much more polite to spell out the object as "Önt ki figyeli?" and similar.
What about "Ki vigyázza rá"? Because I would interpret this as "who is watching him (a child)?"
I understand where you're coming from... in American English we would say "The babysitter is watching the children" (and I think in Brit. Eng. they say "minding the children"), so when I saw the English sentence "Who is watching him?" it's more natural for me to assume someone is asking a parent who is watching their child.