Your email made me wonder whether we have somewhere a list of applications using the MediaWiki API.
It doesn't sound like it is using the API. It probably wouldn't make sense for an offline app, but I haven't checked.
Yup. XOWA is an offline app, and it doesn't require API usage. However, it does call the MediaWiki API in certain situations. To be specific: 1) If you're reading text articles only, then it doesn't use any API. (It is an offline app!) 2) However, XOWA allows dynamic download of images. If you view the Earth page, then it can go out and automatically download all images for that page. For this behavior it does use the API to get the image size and url since this information is not always available from the wikitext alone. 3) XOWA can also retrieve images without using the API. It works 95% of the time, but fails when images have extreme differences in width/height (EX: File:Upper and Middle Manhattan.jpg with width=12,591 and height=1,847) 4) Finally XOWA can be used against the image tarballs from http://ftpmirror.your.org/pub/wikimedia/. The API is not used in this case (since the images are sitting on your local hard drive).
Since scenario #2 will probably be the most prevalent usage (it's what I currently use), I'm guessing that makes XOWA an API app. However #1, #3 and #4 means it can work without it (#1 and #4 being for clearly offline situations).
Hope this isn't too much information.