You are on the right track. If you wanted to run it from the command line without using:
$./realrun.sh
then yes you need to put the executable in your $PATH (or sys wide dir as you said) So from the command line type:
$echo $PATH
this will give you a list of the dir's that bash checks for executable bianaries. But I am ahead of myself.
First take that script and highlight it. Right click and select copy. Paste to a plain text text editior and save as (anything really, but put the .sh extention on it) realrun.sh
Then open a terminal and cd to the directory where you saved it. Type:
$chmod +x realrun.sh
test it by running:
$./realrun.sh
(BTW I tried it for fun and it works fine). Then either save it to a dir that showed up is your $PATH or save it to your ~/user_name directory and create a launcher using the full path. Do you understand?
EDIT: I am sorry I reread the title of your thread and I see you also wanted to install it. I didn't use a script to install it. I just went to:
http://forms.real.com/real/player/unix/unix.html
and d/l'd the rpm (select the libc6 2.x RPM as your OS) and followed the instructions at the bottom of the page to install it. It worked without trouble. I then used the script snippit to run it and it didn't crash at all.
Good Luck!