It is the subjunctive, yes, but it is used not because of any incredulity on the part of the speaker but because it is triggered by the verb of wanting, followed by 'que', followed by a change of person: 'Do you want that I make the coffee?'. English could, but doesn't, put it like this, choosing instead to phrase it as 'do you want me to make the coffee?'. This use of object pronoun + infinitive verb, instead of the subjunctive mood, is quite standard in English.
First of all, you have to know about the two moods in grammar -- the indicative, and the subjunctive.
The indicative mood is just that, it indicates something, it states something.
He eats. - Él come.
This is good. - Esto es bueno.
The subjunctive mood is weirdly different. It is not trying to state something, it suggests something, it can express a wish, a condition, etc. or even a hypothetical scenario.
In English, we've heard of/read something like
I suggest that
he eat. - Yo sugiero que
(It would be "he eats"/"él come" in the indicative.)
The children prefer that
this be good. - Los niños prefieren que
esto sea bueno.
(It would be "this is good"/"esto es bueno" in the indicative.)
Familiar? The part "he eat" is in the subjunctive mood and sounds incorrect because we're so used to the indicative mood. In English, the subjunctive part is usually after the word "that". But the presence of "that" doesn't necessarily make something subjunctive.
I know that
he eats. - Yo sé que
She thinks (that)
this is good. - Ella piensa que
esto es bueno.
The indicative mood still remains.
The rules for the verb are different in the subjunctive mood in English, and so are they in Spanish.
In Spanish, the verb "hacer" becomes "hago" when used with "yo" ("I") in the indicative mood, but it is "haga" in the subjunctive mood.