No, you wouldn't use the Wolfram|Alpha API for this. You would use Mathematica or Mathematica online to make an API.
The code to do this in the WolframLanguage is :
WikipediaData["Elephant", "SummaryPlaintext"]
This returns the summary for the wikipedia article on "Elephant". We can create an API to do this with just one line:
CloudDeploy[APIFunction[{"Title" -> "String"}, WikipediaData[#Title, "SummaryPlaintext"] &], Permissions -> "Public"]
There is also a function called EmbedCode which produces Python code that will call an automatically generated API. You can learn more about these functions in the Wolfram Language documentation:
http://reference.wolfram.com/language/ref/EmbedCode.html
