The Steam Deck is a success compared to previous attempts by Valve, but perhaps not as much as the initial excitement would have you believe. To put things into perspective, some source[1] estimates that a total of 3 million Steam Deck units will have been sold by the end of 2023. The Nintendo Switch, which probably inspired the Steam Deck, has sold 125 million units by March[2]. This amounts to 20.8 million units per year.
You're comparing sales of a product in a nascent category (PC gaming handhelds) produced by a company with near zero retail presence with a marketing campaign almost entirely focused on their existing (Steam) user base to Nintendo, a long standing retail giant that has dominated the market for decades who follow an entirely different business model. That's not to say they're incomparable, particularly in how they provide value to consumers, but there's a whole lot of context that makes the business case more complicated.
Valve might not directly profit from the sale of GPD, Aya or Asus PC gaming handhelds, but they still get their percentage from every Steam software sale made on them, other stores notwithstanding but lets face it, they continue to dominate that space. It highlights that it's not specific hardware that Valve care about as much as broadening access to their storefront.
It's not the hardware itself you should be keeping an eye on, but rather how many platforms on which Steam is available.
> Valve might not directly profit from the sale of GPD, Aya or Asus PC gaming handhelds, but they still get their percentage from every Steam software sale made on them
But those handhelds, being quite expensive, almost certainly sold much less than the Steam Deck, which itself didn't sell overly well.
You're missing the point, it's not Switch vs Steam Deck, or even Switch vs Steam Deck and PC Gaming Handhelds.
It's Switch vs. Steam, which is available on desktop, laptop and handheld form factors and in the future likely a lot more (see box86/FEX, Chromebooks, Deckard). Valve doesn't care where you buy your games, they care that you buy them from Valve.
Valve don't need Steam Deck to become as big as Switch, Steam as a whole already is.
When you buy an Xbox game, you're buying a PC game. Both Sony and Microsoft's first party output are available on Steam. You can run Microsoft Office on an Xbox, the Steam Deck by default has the UX of a console. Sony and Nintendo are the only companies sticking close to their roots, but as mentioned, even Sony is letting that slip. "Console wars" is a misnomer, an old label inherited from the Sega v Nintendo days, it's not that simple anymore.
Windows isn't the "winner" because Windows isn't an app store, Microsoft don't get a cut of every game sold on Windows, but from sales through their store. That's the revenue stream that matters, moreso than how many Xboxes or windows licenses they sell.
You're not wrong that a lot of people don't see things this way. But they, particularly regulators, probably should.
[1] https://www.gamesindustry.biz/omdia-steam-decks-total-consol...
[2] https://vgsales.fandom.com/wiki/Nintendo_Switch