It should be noted that the use of images as maps comprises two parts:
entering the data, and viewing the data. I don't believe either one is
currently possible, though I could be wrong. For data entry, I think the
easiest way to add support for it would be to modify either the
"openlayers" or "leaflet" input types in Page Forms to allow for using an
uploaded image as the map - both OpenLayers and Leaflet inherently allow
for such a thing. And for viewing the data - Semantic MediaWiki has a
"leaflet" result format (via the Maps extension), while Cargo has an
"openlayers" format. Both could similarly be modified to allow for
displaying query results on an uploaded image.
It should be noted that, about ten years ago, both entry and viewing of
image-based maps were possible, via the extensions then called Semantic
Maps and Semantic Forms. This is one of those features that just stopped
being supported, due I guess to lack of interest. Which is too bad, because
it does seem useful for a lot of different applications. But it never
really got usage before. Maybe now is a good time to bring this feature
back, if enough people show an interest in it.
I should also note that there's an extension called Semantic Image
It lets you both add and query data, but the data it deals with is
rectangles on an image and not points, so it may not be what you're looking
for. Maybe it's fine, though.