So, we should define terms. To "dominate" should mean to sell more than or make more money than the competition, which may include taking market share from the competition. I don't doubt valve will continue to make money in an absolute sense, it already does and this likely doesn't change that.
Steam already has a monopoly in the PC space and has the "exclusives" you talk about, essentially games that never were ported to the PS5 or the switch. Thus, in order for the steam machine to take market share from the other consoles, you a) have to take console share from those players, likely by pressuring those developers to port from the consoles to PC. That could be something, but no doubt that pressure already exists, as steam already exists. I don't see how the steam machine changes that. In fact, the opposite situation exists which is why steam makes so much money, as you said. To actually dominate, it can only happen after situation c) below.
New customers or dollars cannot come from people who have a PC and can now forgo using their pc for gaming (by neglecting to upgrade their pc to keep up to date to play new AAAs), as the assumption here is they are selling the consoles at a loss (which may not be true, we'll have to find out). That if anything, is essentially a soft form of b) cannibalisation. So that isn't really "gaining market share" more so than it's changing the means of consumption of the same thing. Moreover, if they choose to sell at a loss, then I only can imagine this leading to actual cannibalisation from their existing PC customers as there isn't really any actual profit being made here.
So finally, the only route they have to expanding their player base in my mind is c) new gamers, that is casual phone players or other non-enthusiast gamers who don't really play games but will be willing to buy a console. This is how the Wii excelled in its generation and how the switch won the last one. Here, it all comes down to price and thus how much Valve is willing to sell at a loss or otherwise subsidise the steam machine using steam proper. So, this to feels like their only real route to "dominating."
As I alluded to above, a) can only happen if c) happens, as Steam already has the mindshare it does and thus it already has the same allure to developers as is the case today, and those developers are still pursuing exclusives with the PS5 and the switch. Thus, if certain developers or games are stuck on the switch or the PS5 with current conditions, they won't move enmass to the steam machine unless c) happens first and thus their calculus changes. And of course, selling at a loss means that they also run the risk of only b) occurring if they don't gain enough new players fast enough to offset the loss from selling consoles.
That leaves them not selling the hardware at a loss, then I don't really know. It's just the steam machine will likely be north of 700 usd if you're not subsidising it, and like the steam deck it will be a novelty item they may or may not make a profit off of. That I wouldn't call "domination", although they may make money overall so I don't doubt they will end up happy.