In response to a Tweet from Jammie Marris, an Xbox 360 fan who regularly plays FIFA and Call of Duty, who asked regarding "the ability to share in-game screenshots to say social networks," Head of Xbox Phil Spencer says the following in a reply Tweet:
Yea, this is the list for the monthly updates, team is making great progress on the updates. More features to come.
Others have responded to Spencer's answer, clamoring for remote downloading, pre-ordering digital games, and PNG support for screenshots on Xbox One.
With Microsoft having updated the system with Party Chat, Twitch streaming, friend notifications, and a sound mixer, we can expect that capturing and sharing screenshots is indeed just one of the features in the long queue of updates.