Yup. My bad. It was the video not liking my browser. Good catch. Coming back to the problem, It looks bad. But wont kill your tranny yet. Logical thinking cap on. The kind of flow suggests nothing ugly like a seal broken. That wont create such continuous nice flow. It could also leak slowly while stopped. Since it is hapenning while the engine is on, tranny fluid running, and taking your word for non leaking while off, my expectation would be on the top side of the transmission. Allison has couple of sensors on the top side and an overfill pressure relief valve that blows with too much fluid. Instead of me defining Allison based on all possibilities, why dont you tell me the exact sequence of your action which led to the problem and may be I can help solve it or guide you towards the cheapest solution.
Also to start with, you will have to pull out your bed and the platform to expose the engine and top of the tranny.