You're not doing something right then. First, you shouldn't need to use Sudo just to install Realplayer(I don't think). I had to boot a Live CD for another reason, so I decided to install Realplayer, and post exactly what I did, to see if it might help you.
To run a command as administrator (user "root"), use "sudo <command>".
See "man sudo_root" for details.
ubuntu@ubuntu:~$ cd /home/ubuntu
ubuntu@ubuntu:~$ chmod a+x RealPlayer10GOLD.bin
Extracting files for RealPlayer installation........................
Welcome to the RealPlayer (10.0.8.805) Setup for UNIX
Setup will help you get RealPlayer running on your computer.
Press [Enter] to continue...
Obviously, you need to CD to the directory where you downloaded the RealPlayer10GOLD file.. I downloaded it to the /home/ubuntu folder.
Also, when you do the ./RealPlayer10GOLD.bin, pay close attention to capital/lower case letters. It won't work if you use all lowercase or uppercase. The Path is also very important, if you're not sure exactly what it is, right click the .bin file, properties, and copy where it says "location" after the CD command in terminal.
After it installs, it should make a realplayer directory then just open it and click, click on Realplay, go through the setup wizard. Try running it w/o sudo, I don't think that would cause your problem, but it might.
Hope that helps, and now I'm going back home, mission complete..