Have you considered installing MySQL with homebrew (http://brew.sh/)? MAMP stands for Mac-Apache-MySQL-PHP (the last part of this being the most important). I would suggest just installing MySQL directly on your box (homebrew takes care of all the heavy lifting) and afterwards I doubt you'll have any difficulty installing that gem.
To install homebrew --
ruby -e "$(curl -fsSL https://raw.github.com/Homebrew/homebrew/go/install)"
Run brew doctor
follow any instructions and then afterwards to install MySQL run brew install mysql
and follow any of the instructions it provides for setting up a user, etc...
============= UPDATE ==============
SO, what you'll want to do is use brew this way to install MySQL and then install the gem in the normal fashion - sudo gem install mysql2
assuming this works, then you will be able to switch back to the old MySQL install through MAMP via -
sudo nano /etc/paths
then add this line to the top of the document -
/Applications/MAMP/Library/bin
restart your terminal and then run mysql
to double check that you are using the MAMP installation of MySQL, and you'll be good to go.