This is quite easy, just find a screen capture software that allows streaming, and get it recording while you play. Although it wasn't with games from GOG, and wasn't streamed, my videos show that it is very easy to capture DOSBox footage. I use Microsoft Expression Encoder 4, which is free for unlimited capture time, the resolution is unlimited, I usually do 720p or 1080p, and it's by Microsoft! You occasionally get prompted to buy the pro edition, but they closed that down a few years back.