First and foremost refer to the manual for C3. https://www.scirra.com/manual/175/google-play
It should explain things clearly enough.
Google play will only work on mobile, in an exported application (not on preview).
In regards to issues with Construct 3, please visit the bug database and make sure your bug was not already reported.
If it was, you may add informations as comment to the ticket.
Otherwise create a new report and fill all the informations required to allow our devs to investigate in order to fix in the next releases of Construct 3.
I tried following the steps there, but there are some things not clear for me. Should I link my app to web or to android or both? I can find my client secret on google play, but I don't know where to add it in my game, as the Google Play object has no Client secret field to add it. It only has client ID, application ID and Game ID. Also even in preview, it seems that Sign in works, but Sign Out doesn't work, which confuses me as it is just a matter of pressing 2 different buttons...