Using both the device's App Store and the Mac/PC's iTunes failed for me. It never offers me v2.1.3. Is there anything I need to do to request that version from Apple?
The version on the App Store just tells me that iOS 6 is required. It does not provide me with an older version of VLC. I tried following these steps as well without success.
I downloaded various binaries from http://download.videolan.org/pub/videolan/vlc-iOS/, added them to iTunes, added them to the device and hit "Apply". All versions that I tried (1.0 to 2.1) all failed after copying and "Installing..." to my iPad first gen.