The G minor harmony is a very standard harmony on the guitar. The harmony truly contains two notes that can be played on open strings (G and D), which suggests that you can indeed play the Gm harmony as an open harmony (see the essential shape in the image underneath). Regardless, the open transformation of Gm is somewhat wrong and never used. In light of everything, Playing Gm as a bar harmony on the third fret, is an essentially more run of the mill technique for playing the harmony.