You’re diving deep into Ghost territory here 
Ghost authentication works via a “magic link”. You can quite easily trigger that from a 3rd party app using this API endpoint:
/members/api/send-magic-link/
(You can observe the payload by triggering that request from the portal while opening the network tab in your browser’s developer tools)
Now, the user will receive a link, which, when opened, requests a session and sets a cookie in the browser.
The big question is how you would port that onto a 3rd party app.
As far as I see, you will not be able to do that with the standard tools Ghost comes with. You’ll have to dig into the Ghost core and do some modifications on the server itself, potentially creating an additional API endpoint specifically for this 3rd party authentication.
Given all of this, I would like to point out this reply from the other post you opened:
Ghost as a platform might not be ideal for your plans of integrating your content into smart TVs – I am sure it can be done, but any modification of the Ghost core always mean ongoing need of maintenance, when new Ghost versions come out.
Quick addition: have a look at this blog post I just found, which goes into a bit more detail on the authentication process: How members authentication work in a Ghost blog? A deep dive into Ghosts open source