Sounds like the audio that OBS is capturing is not the same that TS is outputting on.
A common thing I have seen is that you have the game and it outputs to windows default. You then have OBS capturing windows default. But you wear headphones, so you point windows default to use the headphones. Then in Team speak you have it to bypass windows default and go straight to headphones.
Because TS never went though the windows default and thus OBS never hears it, it is bypassing the OBS capture, even though at your end you are getting both sounds though the headphones
Looking at your images, it may be that it is flip-flopped around, it might be the game and the OBS capture that is listening to something else and you have two routes of audo that end at the same place that you hear, but OBS still hears one and the other one bypasses
