In this situation, are you allowed to turn right after making sure that this manoeuvre, will not obstruct other traffic users?

In the video you are approaching a junction with traffic lights in town; traffic lights S-1 at the right edge show a red light, there is sign D-6 next to them, and a silver car is driving across the junction. You must not turn right, even if you make sure that you will not obstruct anyone - red without a green arrow prohibits entry in every direction. The answer is: no.

The Regulation on road signs and signals states that the red signal of traffic lights S-1 means a ban on driving beyond the traffic lights. A right turn on red is possible only when traffic lights S-2 show a green arrow at the same time - and even then only after stopping and on condition that you do not obstruct other road users. There is no arrow here, so you wait for green. The Road Traffic Act requires you to obey light signals even when the general rules would indicate a different way of behaving. You stop before the line or the traffic lights and move off only after the signal changes.

Legal basis: § 95 para. 1 point 3 and § 96 para. 1 and 3 of the Regulation on road signs and signals; Art. 5 para. 1 of the Road Traffic Act (Prawo o ruchu drogowym)