Google Maps Android API v2 does not currently have the equivalent of the MapsEngineLayer found in the JS API.
However, you can add arbitrary fragments using TileOverlay, and then use the WMS endpoint of your published and open Maps Engine map.
You can find example code for this, including converting WMS requests to tile requests, at https://github.com/saxman/maps-wms-tiles-sample
There is also a video at https://www.youtube.com/watch?feature=player_embedded&v=U6ZbHAXPnhg that demonstrates how to do this, including an example that is extracted from Maps Engine.
Alternatively, you can use the Maps Engine API to transfer functions in the form of vector data (in this case, the GeoJSON format) and draw them on the device, instead of having images for the Engine Engine Karting, however it will performance click when you draw more shapes.
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