If it only shows the option for DSLauncher, start the game, tab out and refresh the selection window. If think that's what I had to do when I played around with OBS the first time.
It records good enough but it uses all my CPU, my computer fan goes to full power and this worries me. Ah, and after some seconds the video goes to lag. Also it alerts me that it's using more CPU. It's my poweless pc. If I could have any good pc I would do some Discovery freelancer videos...
Reduce the recording resolution. If you have a HD monitor, just allow OBS to record in 0.5 screen size and make sure you have the chatfont on normal or big. You won't produce High-Quality videos like Seafalcon does, but I doubt there are too many people that are watching Freelancer videos anyway. *cough*