The Jagex launcher and Jagex Accounts will not be supported on the Linux OS.
If you wish to continue playing on a Linux machine you will have to use a mechanism that enables Windows applications to operate. There are community projects available that you can try such as:
- TormStorm's jagex-launcher-linux project on GitHub
- This Reddit thread in r/2007scape discusses the process
- A YouTube guide by c00k
Jagex is not responsible for the maintenance and safety of content produced and hosted by third parties and any use of third-party sites is at your own risk.