Holiday 2007: Microsoft launched a program which allowed Xbox Live users to send each other Microsoft Points as a last minute gift.
Sometime between then and now the gifting feature, which was in “beta”, got canned. I remember going through the cumbersome process before. You couldn’t directly send points from one Gamertag to another, you needed the recipient’s linked Windows Live ID. Still sort of useful for eleventh hour gifts. Supposedly, the team was working on Microsoft Point gifts via Gamertags, but since the gift points feature vanished without warning don’t count on that coming.
That leaves Nintendo as the only console around with a downloadable game gift system unless you count game sharing over PSN.