I've enjoyed the mobile app so far. Playing on the Samsung Galaxy Note 8 is awesome. I also use my phone as a PC in DeX mode. And regularly connect it to a monitor. It would be cool if osrs mobile had an option to put it in desktop orientation and have support for keyboard and mouse. This would be an awesome feature addition.
If you want to play your OSRS game from a pc, you need to add a login/password to the account.
Add a login email to Google created accounts
You can then use the Old School desktop client.