I recommend you consult the technical specification of that device and look up, if NDI is supported. (I guess: no).
Not using OBS as streaming client but send its output to some other device to stream from there isn't what OBS is designed for. OBS is a streaming client itself. You throw away the feature OBS is made for in the first place. So if you want to stream some hdmi signal, I recommend you get a simple hdmi capture device, read it with OBS and stream with OBS.