It seems like Valve has re-uploaded without the emulator, but I think there's a case to be made that this sets expectations for Valve and Nintendo in an important way.
Valve is not selling a walled garden product and if you are expecting them to administer the steam deck like one you will be disappointed. If that's not for you then you should not go into business with Valve - it would be painful for both parties.
Nintendo doesn't have a relationship with anyone (content creators included), apart from their lawyers.
Despite the video being retracted the desired effect has been achieved. The flurry of news has more lay people thinking about the Steam Deck in the same class as the Switch, even if their intent is not to emulate.
Sometimes when you have a sensitive relationship, it can be helpful to support the thing that makes the other company uncomfortable without openly advertising it.
what relationship? Valve is pretty much PC only other than some ports of old source engine games. Nintendo is first party console and handheld with couple of iOS/android apps. their isn't really any relationship to be sensitive.
No one is abusing the legal system. They're using the legal system. The way to fix it is not to try to stop people using the system 'wrong', but to update the system so it's appropriate for modern tech.
While that's strictly true, morality is not the same as the legal system. Using the legal system in ways that other see as immoral does not and should not make friends.
Do they have that much of one? I think they've had one Switch title (the Portal collection) and Nintendo doesn't really have anything on Steam as far as I know.
Even then the relationship more Valve repo acces and licencing > Nvidia's First Party Studio > Nintendo. And obviously Nividia has a good relationship with Nintendo because of the Tegra X1 powering the switch so it's not a situation of Valve communicating with Nintendo as much as it's Valve letting Nvidia make ports out of their back catalog by occasionally going "I will allow it" whenever Nvidia Lightspeed Studios asks politely enough.
I would guess its much more subtle than this. Consider potentially nintendo refusing to port games that were on steam, or demanding more money/control over games that have overlap with steam.
Punishing publishers for choosing to release on a competitors platform they don't like would hurt those publishers more than Valve. Nintendo's relationship with third parties is already often strained, doing anything like you suggest would in particular cause indies, which Switch relies on to fill the gaps between Nintendo releases, to flee the platform.
Valve is not selling a walled garden product and if you are expecting them to administer the steam deck like one you will be disappointed. If that's not for you then you should not go into business with Valve - it would be painful for both parties.