Are you obliged in this situation to reduce your speed?

In the video you are driving along a town street towards a pedestrian crossing marked with sign D-6 with plate T-27, with a traffic island and bollards; there is no pedestrian on the crossing or near it. You are not required to reduce speed. The answer is: no.

The Road Traffic Act requires a driver approaching a pedestrian crossing to exercise particular caution and to reduce speed so as not to endanger a pedestrian who is on the crossing or entering it. So the duty to reduce speed is linked to a pedestrian - you have to slow down enough not to endanger a person who is on the crossing or entering it. When the crossing and the area around it are empty, as here, the rule does not require slowing down for its own sake; what applies is particular caution, that is increased attention and readiness to react, and of course the speed limit in force on this street. The Regulation on road signs and signals puts it the same way - with reference to pedestrians on the crossing or entering it. Plate T-27 warns that the crossing is used by children, so particular caution also means a speed from which you can stop in time if a child comes out from behind a bollard.

Legal basis: Art. 26 para. 1 and Art. 2 point 22 of the Road Traffic Act (Prawo o ruchu drogowym); § 47 para. 4 and 5 of the Regulation on road signs and signals