In this situation, are you obliged to stop in front of the railway crossing?

You are approaching a level crossing with barriers. In the video, the barrier is just coming down - it has started to come down, so driving onto the level crossing is prohibited. You are obliged to stop before the level crossing and wait until the train has passed and the barriers have been fully raised.

The Road Traffic Act prohibits driving around lowered barriers and half-barriers and driving onto a level crossing if they have started to come down or have not finished rising. Even when the barrier is already high, you make sure that no train is approaching before you drive onto the tracks. Driving around a barrier that is coming down is one of the most serious petty offences on the road.

Legal basis: Art. 28 para. 1 and para. 3 point 1 of the Road Traffic Act (Prawo o ruchu drogowym)