Can I use Themeframe on Linux Mint desktop OS?

Hello,

I am running Linux Mint and notice that requirements are either Windows or Mac. However notice that Xampp is an option for local web server. Am I able to use Themeframe on my Linux machine?

Thanks!

Yes, of course.
Just use XAMPP 1.7.1 because this version of XAMPP includes:
...
- PHP 5.2.9

Set XAMPP, it's not difficult:
sudo tar xvfz xampp-linux-1.7.1.tar.gz -C /opt

then
sudo /opt/lampp/lampp start
then
sudo cp -r themeframe126 /opt/lampp/htdocs

and
cd /opt/lampp/htdocs
ls
sudo chmod -R 0777 themeframe126

So, http://localhost/themeframe126

Do not forget
sudo /opt/lampp/lampp start
sudo /opt/lampp/lampp stop
sudo /opt/lampp/lampp restart

I hope everything will work.
Good luck.