Is there a standard file format for Magic the Gathering games?
Right now, the closest thing to an "industry standard" for sharing games is video, using services such as Twitch TV and YouTube. This is how Wizards does event coverage and how many Magic writers share their games.

Players often record their voice as they play or go back later and add commentary. Here is a fairly typical example.
Magic Online keeps a history of game states that could be used for replays, but access to the data has generally been limited (leading to players resorting to engine quirks and workarounds to get at it). Last I checked, the data's still not easily accessible, nor is it very portable or shareable.