Yes, you can buy fonts for someone else. The license will be in their name and they will be able to use the fonts just as if they had purchased them. They will not, however, be able to upgrade the order themselves, but you can upgrade their order any time.
To make a purchase for a licensee other than yourself, simply specify the third party as the licensee during checkout.
Once the order is complete, you can download the fonts and provide them to the licensee — they will not have access to your account or a download page.