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You can add this option to your table as well - using a loopback cable. Here are details from Google if you want to make your own:

• https://source.android.com/devices/audio/loopback.html
  
  EDIT: ok, this loopback capability seems to be included in the Mobizen headset that you mentioned:
  
  >You could also buy this headset and use it with a Mobizen app. A "world first" that shouldn't even have to exist!
  > - https://www.amazon.com/GameDuck-Mobizen-Recordable-Headphones-Comfort-Fit/dp/B01KZM6KM4
  
  Basically you plug this into your android device's earphone jack. The output pins are routed to the microphone input pins. So whatever is playing is going to be audible if you record. The quality will be better than off the air. However, it still is not "digital" internal audio as you require - but it will be good enough for everyday use.
  
  One of the ways many Android devices prevent audio recording is by doing some type of heavy echo cancellation even for over the air recording (i.e. using microphone to record what is playing out of the speaker). One of the primary targets of this strategy is to prevent call recording it is generally suspected - so for most North American models, you will find call recording does not work well (there is very heavy echo cancellation type effort to remove the speaker audio from the microphone).
  
  Newer Samsung devices even from non-North American regions are starting to have this limitation (example: Samsung S7 after android update, and S8 etc.).
  
  As other poster reported, android in general does not allow apps to have access to the internal audio - although as you said, on some phones that does seem to work reasonably well (whether that is actually recording digital internal audio, or just the microphone recording off the air and through the body what is being played on the speaker).