Buying and sending games as a gift digitally isn't available on all platforms, but Microsoft promises to include this feature on the Store in the future, and it looks like they may deliver this in the next firmware update.
Some Xbox Insider Program members have reported a new button to "Buy as Gift" on Xbox One or Windows PC, and it's said that only those with access to the 1710 system version are allowed to send a gift to another person. It could be someone on your friend list, but also you can just type an email address as well.
Windows Central editors are among those with access to the gifting system, and they explain that the checkout process is exactly the same as usual. If you choose to send it via email, though, your friend will get a 25-digit code to be redeemed at the Store.
Microsoft hasn't announced a release window for the Buy as Gift option, so we can't confirm that it'll be included in the global version of the next firmware update, but we hope it is. Is this a feature you've been wanting?