The initial gifter doesn't have the option but the one he/she gifted the link to when redeem the initial gift link to their email, they can then forward that link to someone else if they haven't redeemed the game yet. It will still work because the game is unredeemed to any particular steam account.
I really did not fully understood this explanation so I made an experiment and confirmed this.
When a person gets a gift from HB they to redeem it on the HB site with an email.
If the email is not registered with HB then they get an email with a new link the same kind you get with any HB purchase.
That second link let's you download a game or redeem a game to Steam and it could easily be forwarded to someone else.