It's not like a web browser where it's up to the user to find the services who host the content they want. Yuzu is accessible as directly as anything on Steam is, using systems and services (Discover and Flathub) Valve made a conscious choice to implement. They aren't hosting Yuzu on their own servers, but they are providing direct access to it.

Putting Yuzu into marketing materials was definitely a bit of a faux pas, but it's also one of those occasions that highlights the absurd pageantry of pushing the narrative that emulation is taboo. It's in the video because there are those at Valve use Yuzu on Steam Deck themselves and normalizing that is a net good.