Wine may take some work to get Windows applications to work with, it usually pays to read up on the AppDB entry for the game over at WineHQ (http://appdb.winehq.org/
Installing Windows inside Oracle VirtualBox may work better as that offers a true virtual machine (you'll have to configure it properly to share 3D hardware and such).
BTW, this is not magically different on Ubuntu--you can also install Wine or VirtualBox on Ubuntu, but any other virtualization software you could download or purchase for on Ubuntu (like VMware) would run also on Linux Mint. Linux Mint is based on Ubuntu, so anything that works in Ubuntu works in Linux Mint. But use whatever works for you
Like keet shared, the Ubuntu installer will happily erase your hard disk during installation.