In this situation, do you have priority over the vehicle travelling in the opposite direction on the right?

In the video you are waiting in a town in the left-turn lane before a junction with traffic lights; the green light comes on, and a dark car turning right is coming from the opposite direction. You do not have right of way over it. The answer is: no.

The Road Traffic Act states that the driver of a vehicle, when approaching a junction, is obliged to exercise particular caution and give way to a vehicle approaching from the right, and if he is turning left - also to a vehicle coming from the opposite direction going straight on or turning right. The green light gives you the right to enter the junction, but it does not decide right of way between vehicles that have entered on green from opposite directions - this is decided by the general rules, and they require a driver turning left to give way to anyone coming from the opposite direction who is going straight on or turning right. The car from the opposite direction is turning right, so it is going into the same street as you; if you turned first, you would cross its path. So you enter the junction, stop in the middle without blocking traffic, let the vehicles from the opposite direction pass and turn when there is a gap or when the amber light comes on and they no longer enter.

Legal basis: Art. 25 para. 1 and Art. 5 para. 3 of the Road Traffic Act (Prawo o ruchu drogowym)