I wonder whether the documentation actually means the viewport aspect ratio instead of the screen aspect ratio.
If a camera has no aspect ratio set, it is maybe intended to use just whatever aspect ratio the viewing application has, no matter whether that is SketchUp, or another application.
In the Ruby API, you would get it from
#vpheight, but I didn’t find a corresponding method on the SDK side. The SDK is focussed on importing/exporting (eg. .skp writers without SketchUp running) and does not expose all methods that one would use for writing a tool that interacts with the viewport.
When SketchUp is running, you can access SketchUp’s Ruby API through a Ruby C extension, but I don’t know if/how that can be integrated in combination with using the SDK.