Your point regarding species extinction is a good one. However, in languages, "extinct language" has a more specific meaning. See http://en.wikipedia.org/wiki/Extinct_language .

I believe that language extinction occurs when it's possible to point to the last living speaker of the language, or more generally, when there is no modern version of a language.

But you are right that the person who asked the question is more likely to think of the more transitional, biological meaning.

You may like this clip where Eddie Izzard goes to Friesland to "buy a brown cow" in Old English. https://www.youtube.com/watch?v=OeC1yAaWG34