looks like the update is not in the repo yet, did
apt-get update
and it says runescape-launcher is already the newest version (2.2.4) when trying to update it
You won't find an update via apt for RuneScape unless we update the launcher, which we haven't needed to do in a long time. Version 2.2.4 refers to the launcher. The latest client version is downloaded automatically when you start the game.