Yes. To play on both platforms, you need to buy two copies of the game, one for each. (There's still only the one monthly fee, though. At least the extra expense is one-time-only.)

Buy a Windows version of the game. Then go to the Mog Station website, log in with the account created on PS3, select "Account Services" and then, under your service account, select "Add Windows Service". That's where to enter the code you'll get with the Windows version.