Conversational Postulate

In two fields that I've worked I've heard the term "Conversational Postulate" used to refer to a yes/no question that is expected to elicit some behaviour in the listener.

Questions such as "Can you close the door?" used in place of "Close the door please".

I haven't been able to find a reference to the term outside of those fields.

Is there a standard categorisation in English for the kinds of words that are yes/no by nature but are pragmatically understood to require some action?

In addition to the allofunctional implicature article mentioned by Mark, see the illocutionary act article in wikipedia:

Illocutionary act is a term in linguistics introduced by John L. Austin in his investigation of the various aspects of speech acts. We may sum up Austin's theory of speech acts with the following example. In uttering the locution "Is there any salt?" at the dinner table, one may thereby perform the illocutionary act of requesting salt, as well as the distinct locutionary act of uttering the interrogatory sentence about the presence of salt, and the further perlocutionary act of causing somebody to hand one the salt.

The performative utterance article mentions some other theories about performatives and causatives. Note, the latter link may address your question about "standard categorisation in English for the kinds of words that are yes/no by nature but are pragmatically understood to require some action":

In linguistics, a causative ... is a form that indicates that a subject causes someone or something else to do or be something, or causes a change in state of a non-volitional event.
All languages have ways to express causation, but differ in the means. Some languages have morphological devices (such as inflection) that change verbs into their causative forms, or adjectives into verbs of becoming. Other languages employ periphrasis, with idiomatic expressions or auxiliary verbs. All languages also have lexical causative forms (such as English rise → raise).

Allofunctional implicature is one way of expressing this concept.

A classic example would be the "question": Could you pass the salt? In the above sentence, although it is grammatically structured as a question, it can quite safely be inferred that the speaker is not inquiring as to whether the person they are addressing is physically capable of passing the salt at the dinnertable or not. What the speaker really wants is to get the salt.