Gist to install Sublime Text 3 on RHEL 6 +

sublime-text-3.sh

#!/bin/sh
SHORTCUT="[Desktop Entry]
Name=Sublime Text 3
Comment=Edit text files
Exec=/opt/sublime_text_3/sublime_text
Icon=/opt/sublime_text_3/Icon/128x128/sublime-text.png
Terminal=false
Type=Application
Encoding=UTF-8
Categories=Utility;TextEditor;"
SCRIPT="#!/bin/sh
if [[ \${1} == \"--help\" ]]; then
/opt/sublime_text_3/sublime_text --help
else
/opt/sublime_text_3/sublime_text \$@ > /dev/null 2>&1 &
fi"

echo "Downloading Sublime Text 3..."
curl -L "https://download.sublimetext.com/sublime_text_3_build_3143_x64.tar.bz2" -o "/usr/src/Sublime Text 3.tar.bz2"

echo "Installing Sublime Text 3..."
echo -ne '#####                     (33%)\r'
cd /usr/src
tar -xvjf "Sublime Text 3.tar.bz2"
echo -ne '#############             (66%)\r'
cd "sublime_text_3"
mv -fv "/usr/src/sublime_text_3" "/opt/sublime_text_3"

echo "${SCRIPT}" > "/usr/local/bin/subl"
chmod +x "/usr/local/bin/subl"
echo "${SHORTCUT}" > "/usr/share/applications/sublime-text-3.desktop"
ln -s /opt/sublime_text_3/sublime_text /usr/bin/sublime3
echo -ne '#######################   (100%)\r'

# Package Control - The Sublime Text Package Manager: https://sublime.wbond.net
echo "Installing Package Control..."
wget --no-check-certificate https://sublime.wbond.net/Package%20Control.sublime-package
sudo mv Package\ Control.sublime-package "/opt/sublime_text_3/Packages/"
cd .config/sublime-text-3/Installed\ Packages/
wget https://packagecontrol.io/Package%20Control.sublime-package

echo "Finish!"

Great!
There was another new update : Build 3083
I believe it to change the file to be downloaded as well.

[UPDATE] Line 18 - http://c758482.r82.cf2.rackcdn.com/sublime_text_3_build_3083_x64.tar.bz2

Fixed the Tarball link and updated the gist to the latest 3103 build along with all of @ThePhoenixBird's fixes! 😄