Well this is more an animation problem then a GE problem … and facemania’s solution might work on animations that don’t use the armature object but when animations are keyed in without the rotation being applied to the armature you’re in some deep … problems …
Because the bones are evaluated using quaternions and not Euler angles it is almost imposable to fix the Rotation Not Applied Before Animating Syndrome (RNABAS) … especially when there are rotation keys (quats in the pose IPOs) …
It is almost imposable to fix quats that have the wrong axis orientation so you might have to redo all your animations … but this suggestion should work as a workaround for your predicament :
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clear the rotation with Alt-R on your armature (and your mesh too if you want but if it follows the armature and the animations play ok you don’t have to do this)
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from the top view space -> add -> Empty
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hit A to clear selection then select your armature then shift-select the Empty and Ctrl-P and parent the armature to the Empty
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now rotate the Empty until your armature is oriented like it was before you cleared the unapplied rotation
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hit P and see if it worked
I’m not sure if you will have to make the empty a part of the game (I don’t see why) …
Hope this helps .