Same problem - hang on 'Loading application resources' (but really, it's just trying to run the client binary). I have two desktops with RS, both Ubuntu 20.04. After the update mid-day Feb 25th: one hangs, the other starts OK (but newest version seems to hang mid-play occasionally). The former is on Intel i5 built-in video, the (somewhat) working one is a notebook with NVidia graphics.
Here's what I found (technical stuff follows): runescape-launcher downloads and runs a binary ~/Jagex/launcher/rs2client. This is the thing that now wants to use libopengl0 and libegl1 that some have found to be absent - runescape-launcher itself doesn't depend on these, so they won't be auto-intalled by it; I had them installed for other things.
If you have the missing library problem, just install them - it may work.
The new (Feb 25th) rs2client deadlocks on starting. I sent it ABORT and collected the core dump. On brief examination, the thread picked as active by the debugger hangs on a mutex, apparently somewhere in the libEGL_mesa library. Seems like a problem in that library or in how RS is using it. Or maybe in the underlying DRM driver that controls the video (this may explain why it works for some).
I will dig some more, though my skills in this are rusty nowadays. On intuition, this hang isn't something that can be resolved with updating the system, configuration or deleting cache or anything simple.
Mostly hoping RS can find and fix this, in the meantime I'm stuck playing on the laptop.
26-Feb-2021 19:46:49