Given the google api displaying a map on some site with layer 'A' on top of it. How can I create a GIS file for layer A (as simply as possible of course)?
Only the Static Maps API and Google Map Maker (Select Countries) are available to download. (Unless you have an Android based tablet or android phone which can download up to 5 areas)
You can create your own paths, markers with the static API https://developers.google.com/maps/documentation/staticmaps/#Paths
Map Maker Countries are available from https://services.google.com/fb/forms/mapmakerdatadownload/ (but read the terms and conditions) This data is in KML and Shapefile formats
The short answer is you can't. Unless, however, the site has a ftp file transfer set up for downloading from their site. Just like the ortho image layer in google maps, it is being rendered by your browser client from a backend data store but is not accessible through google maps as the data directory is not available to your client.