In the presented situation, do you have the right to enter the level crossing?

Why?

In the video, the red lights are still flashing and the barriers are still rising. Either condition prohibits entry onto the crossing. Wait until the barriers are fully raised and the red lights have stopped flashing, then check that it is safe to proceed.

art. 28 ust. 3 pkt 1 Prawa o ruchu drogowym oraz § 98 ust. 5 rozporządzenia w sprawie znaków i sygnałów drogowych