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.