I'm not a steam user, and what I say here is mostly opinion, but since nobody has yet to chime in, then I will.

I do know that once a key is linked to a steam account, with any game, it is linked for the life of the account and can't be transferred between steam accounts. Steam, according to their terms of service states this. You or your friend might try contacting steam, although I don't know if it'd do any good, as I said above, the key will forever be linked to his steam account.

It is also not possible to use the same steam account one more than one PC.

The only chance that you have, is to aquire a new steam Stormblood key for the game, and activate it in your mog station, since I'm unsure if the mog station will validate which steam account that ARR it's attached to. If mog station doesn't care, then it would be possible, but it would require you to launch the game independent of steam, which I read is possible. However, if you try this, be prepared that you may take another loss and that this may not work. Steam or SE either one are not likely to be of much help, and your only option.