Nintendo Switch has supported video recording for a few weeks now (simply hold down that capture button). It was introduced just in time for the launch of Super Mario Odyssey but only a handful of Nintendo's own games have supported it.
That all changes today with the release of Skyrim, developed and published by Betheseda. The open-world role-player will be the first third-party game released worldwide to support video capture, according to Aussie site Vooks, which has an early copy.
You'll need to download a small day one update to Skyrim in order to unlock video capture, but then you're away. Now, does it still have those backwards-flying dragons?
Update: I've just learned Japan-only Switch game Monster Hunter XX, published by Capcom, also got video capture last night. I've updated this article's headline to reflect this.
Only four other Switch games support video recording: The Legend of Zelda: Breath of the Wild (version 1.3 onwards), Mario Kart 8 Deluxe (1.3 onwards), Splatoon 2 (1.2 onwards) and Arms (3.1 onwards). It looks like any other game which wants to support it will need to be updated first in order to do so.