If you look at satellite images from various mapping services, you can see that this area in Katowice has been built up fairly recently. ul. Tadeusza Dobrowolskiego is adjacent to the new campus for the Silesian Museum. The new museum campus opened in 2015, and ul. Tadeusza Dobrowolskiego is an access road for the museum.
The street itself was officially named on July 30, 2013, which coincides with the period when they were building the new museum campus.
Bing Maps shows the area before the road was constructed.
Mapquest shows a more recent satellite photo than Google Maps.
This is an area with future development plans that have not yet been fully realized. This article from when construction first began in 2011 confirms that the first phase of construction for ul. Tadeusza Dobrowolskiego is to extend from ul. Dudy-Grazca only as far as ul. Nadgórników with future plans to extend it all the way through to ul. Katowicka.
This map shows the intended road layout in the area.