Learn English – Do you want choice A or B? Yes!– Is it wrong to answer with a yes when given two options

Response is a very broad term, and includes all reactions to a stimulus.

Answer is more specifically a response to a direct question.

One can always respond to anything (an event, an injury, a letter, a speech, a question...) but one can only answer a question. As Emanuil said, it's also possible to respond to a question without actually answering it; listen to politicians being interviewed.

First of all, it's common usage, that is, in native English speech, to refer to multiple choices using either, but it's not entirely grammatical (from a prescriptivist's point of view). The definition of either is:

Each of two. [from 9th c.]  
One or the other of two. [from 14th c.]  

Note that I say it's common in informal speech and usage, but probably not for formal contexts.

An entire page of Wikipedia was devoted to this word, and the definition given was:

Either/or means "one or the other." Its usage, versus the simple or structure, is often for emphatic purposes, sometimes intending to emphasize that only one option is possible, or to emphasize that there are only two options.

Thus, it depends on what the context is. If in speech, then either would be appropriate. If however, in a formal context (business letter, etc.), then using either for multiple choices would be inappropriate.