It fails differently for me. I installed it in devmode.
/snap/runescape/x1/usr/share/games/runescape-launcher/runescape: error while loading shared libraries: libcurl.so.4: cannot open shared object file: No such file or directory
I expect you might be missing a path configuration, which you should get from the desktop-gtk2 launcher you’re not actually using.
command: desktop-launch $SNAP/usr/share/games/runescape-launcher/runescape
But even if you do that, the launcher probably expects to be on a normal linux system where it has write / read access in interesting places. So could be fun/challenging to snap.