Try to install using different version, It's happens because sometime binary is not available for specific verion for window.
gem install mysql2 -v 0.2.6
If still you have issues, Try below steps.
1) Download the MySql C Connector from: http://dev.mysql.com/downloads/connector/c/
NOTE Don't download the installer, download the ARCHIVE for your OS
2) Extract the file to C:\mysql-connector
3) Then ran:
gem install mysql2 --platform=ruby -- '--with-mysql-lib="C:\mysql-connector\lib" --with-mysql-include="C:\mysql-connector\include" --with-mysql-dir="C:\mysql-connector"'
It's works for me.