The ability to record the players has been around since launch with the optional "GoPro" or "cell phone" accessories.
1-2-Switch is now at 1.1, with a surprising feature added.
The new software update for the Switch launch title adds the video recording function as seen in other Nintendo published titles. The same restrictions apply on recording, with clips of up to 30 seconds.
Someone at Nintendo reopened a codebase to allow video capture so I could make this video #12Switch #NintendoSwitch http://pic.twitter.com/yS1vX1u56O
Source: Nintendo World Report Updates
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