Windows 8 64-bit
NVIDIA GeForce GTX 765M
Action layers do not appear to work in newer versions of Blender. Actions playing in higher layers should play on top of actions in lower layers (using layer_weight percent of the combination of the layers below). In the current version of Blender, actions playing on lower layers appear to completely prevent actions on higher layers.
Exact steps for others to reproduce the error
Start the game engine in the attached file. In Blender version 2.75 and earlier, the cube should move diagonally as expected (the action on layer 0 moves the cube vertically, the action on layer 1 moves the cube horizontally and uses 0.5 layer_weight). On Blender version 2.76 and later, the cube only moves vertically (only the action on layer 0 plays).