https://help.jagex.com/hc/en-gb/articles/17160273294097-Jagex-Launcher-FAQ
Visit above link and read said page '
Jagex Launcher FAQ
'
Go to the bottom of said page where it says
What if I don't want to use the Jagex Launcher?
Currently, the Launcher is optional if you do not have a Jagex account. Eventually, the RuneScape and Old School RuneScape standalone clients will no longer be supported. If you don't want to use the Launcher just yet, you can follow these links to install the standalone
RuneScape
or
Old School clients
.
These 2 links in said text will allow you to download Jagex's Game Clients without the use of Jagex Launcher which will help you to login the 'Old way'.