RX/TX so you can run it in your back pocket and have your phone go to amp, then amp to headphones. Be aware you aren't using the DAC in this case at all, Just boosting the volume.
Is this better than the award winning Chord Mojo? I do acknowledge the Chord does not have Bluetooth and this does, but for wired listening and using the DAC, is this a better option?
Such cables do exist - they are available from Apple, Amazon, Monoprice, etc. I can't think of any reason they wouldn't work in your situation, although it might be hard to find a really short one for portable use.