Is it proper in this situation to continue driving on the same lane?

In the video you are driving in the left lane of a street in a town with two lanes in your direction; the right lane is taken up along its whole length by parked cars. You are acting in accordance with the rules by continuing in your current lane. The answer is: yes.

The Road Traffic Act requires a driver to keep as close as possible to the right edge of the roadway and, if lanes are marked, to use only one lane. "As close as possible" means as far as conditions allow: when the right lane is taken up by a line of parked cars, the only lane you can drive in is the left one, and driving in it does not break the rules. Moving into the right lane at every gap between parked cars and returning to the left lane would be pointless and dangerous, because each change of lane is a manoeuvre that requires signalling and giving way. When driving in the left lane next to parked cars, you keep a safe lateral clearance from them, because at any moment someone may open a door or pull out, and you watch for a pedestrian stepping out between the cars. When the right lane is free again for a longer stretch, you return to it.

Legal basis: Art. 16 para. 4 of the Road Traffic Act (Prawo o ruchu drogowym)