Nintendo is known for using the full extent of the law to protect its intellectual property. The now-removed video showed off a number of Switch games running on the Deck, including Super Mario Odyssey and Super Mario 3D World, along with performance metrics.
One of the videos taken down, for example, was from YouTube channel The Phawx who also has videos showing Xbox and PlayStation 3 emulation on the Deck. It's not clear who exactly is issuing the takedown requests, but given many of the channels have similar videos showing emulation of other non-Nintendo platforms that are still on the site, one could make an educated guess that it's Nintendo itself. The videos show off the Yuzu and Dolphin emulators running on the Deck, which emulate Switch and Wii games respectively (thanks, Nintendo Life). Videos demonstrating emulation of Nintendo consoles on Valve's Steam Deck are being pulled from YouTube.
