The entire series is doujin in that it is an amateur production. Just like how even the main Touhou series and those made in collaboration with ZUN are "doujin".
Similarly, the fighting game is made in collaboration with Ryukishi07 and 07th Expansion. It's doujin, but it is not fanmade, because its nature as doujin comes from being an amateur project, not from being fanmade.
Also, the fighting game itself is named Ougon Musou Kyoku, while the series for which it is a spin off of is Umineko Naku Koro ni. It's developed by 07th Expansion in collaboration with people who know how to code fighters, so it is an official part of the franchise, though it does not fit anywhere into the storyline specifically, so far as I can tell, nor does it progress the plot.