For people who are signed up for Microsoft Xbox Insider Program, you now have access to the Game Gifting option when purchasing games through the Xbox Marketplace. It's in "preview" mode, a.k.a. Beta, so it's only for those accounts that have signed up for the Insider Program. It'll work very similarly to how gifting games is on Valve's Steam store.
The game that gets gifted can be sent to a friend's Xbox or to their email address, then the person just needs to redeem the code and POOF! The game is theirs! Whether the process stays this way when program reaches public status remains to be seen, but we don't see why there would be any need to change it.