By Mini-PC you mean Netbook, then I doubt it will have strong enough hardware to play the game. Even if it did have strong enough hardware, you still need the CD in the drive to play the game (Legal reasons) so you will need to buy an external optical drive. They are pretty cheap anyway, so that's not a huge problem. I just don't know if your computer can play it.
If the Netbook has an Intel Atom processor, then there is a decent chance it will have a decent enough chipset to at least run the game.
But either way, you do need the DVD to play. If you were really desperate to get the files onto the Netbook, you could send them to the other PC, but you'd still need a disk to play them with.