Do not worry! Since you'll receive a purchase link to complete the gift order, after the recipient has accepted, you have total control over this gift. So, in case it went to the wrong person and that person accepts your gift, simply disregard the purchase link.
You can either copy and paste the link from the "copy of the gift link" email in your inbox and resend it to the correct recipient, or simply start over again and generate a new link. The old link will just expire.
Final note: You may want to let the wrong recipient know that you've sent this gift link by mistake.