The BVH skeleton hierarchy is way different to our skeleton used, animations need to go through a special conversion (it's called “baking”).
So to get them into the game:
The baking starts then on the selected character (highlighted icon on the left panel).
The result will not match to 100% to the pose/animation in the BVH, as of the above reason. It just gives a good starting point for a new pose.
If you're happy with the result, save the pose on one of the local slots. Only after that step the pose will be available within the game.