Back in July, the corporate vice president of Xbox, Mike Ybarra, revealed that digital gifting wasn't "far off" from releasing on Xbox platforms.
Xbox Q&A panel at PAX West, Ybarra was asked when Xbox owners can expect to see game gifting and Wishlists hit the Xbox Store. According to Ybarra, one of the two features is coming "very soon" and the other is on “the list of things we [Microsoft] need to get to.”
Because we know that gifting isn't 'far off,' it's safe to say that the feature is the one coming sooner rather than later. That means that Xbox users will have to continue waiting on Wishlists becoming available on the Xbox Store.
The preview update for Windows updates has already begun including allusions to game gifting on the Windows Store too, which further supports the thought that gifting is coming "very soon" to both platforms.