API talk:Images

I really think this page need a note about how to download the images. "File:19191125 A New Physics Based on Einstein - The New York Times.png" is not exactly downloadable

It's not the most intuitive thing in the world, is it? :) The trick is to get into the MediaWiki mindset. Modules like this one are geared towards finding pages; if you want to know anything about the pages, you usually have to use a different module. The one you're looking for is API:Imageinfo. Tweaking their example, both for your question and so that it actually works, you might use something like this (changing the titles parameter as needed):

https://www.mediawiki.org/w/api.php?action=query&generator=images&titles=MediaWiki&prop=info%7Cimageinfo&iiprop=url

Now that you have the URL, downloading should be straight forward.