It's a big market, but is it really competing with other forms of gaming? As an analogy, if someone were buying up all the oven manufacturers, would it matter that microwaves were more widely used?
But to properly reply to your comment: indirectly, yes. I'd go so far to argue that the rise of mobile gaming yet another reason why the Vita couldn't gain traction (releasing in 2013, around the time mobile games started to really show they can do more than arcade-y style minigames), and why Nintendo decided to pivot to a hybrid model. the 3DS's middling sales (for a nintendo console) definitely put some pressure on even the uncontested king of handhelds, so what chance would any other platform have?
Meanwhile Microsoft in this era would flounder with Windows Mobile and fail to gain traction with Windows 8S or whatever they were trying to do with tablets in this time, so I guess their enthusiasm to try that in their gaming division was negative. I'm honestly still baffled Valve beat MS to making the most obvious Xbox handheld, that we now know as the Steam Deck.
So I'd say it was competing the same way handhelds competed with consoles. There would never be apples to apples comparison, but the markets definitely tug on one another, the markets keep eyes on one another, and the audience have some significant overlap, enough to be kept in mind with marketing. Sony and Microsoft wouldn't be marketing cloud gaming on mobile if they thought none of their audience were interested in playing games on their phone.
Remember that the PSP was also a pretty good multimedia device pre-smartphone. So it lost that userbase as it became the Vita. But of course it's primary purpose was games and the Vita focused on that in its western marketing: "console gaming on the go". It couldn't sell itself on mobile style games if it ever expected to succeed, so while it may have overlap I can't say it was a direct smartphone competitor either.
And it took similar resources within Sony to develop and market it. Another of a dozen reasons why it failed: Sony decided very early on to put all its chips into the PS4, and ditched first party Vita support after the first year. This woildnt make sense for a phone competitor.
As a result, it seems that it's a different market.
Every time I want to play a game I have to consider if I want to bust out my laptop, turn on my TV system, or just swipe over to a game on the phone I'm already holding.
I obviously prefer to play my PC or PlayStation, but will play my Switch if I am in the bathroom, riding shotgun on a long car ride, etc. Mobile games, for me, are essentially waiting room games or something I will whip out if I have exactly 7 minutes to kill.
I don't generally think, "I want to game" and then decide which one is worth the effort in the moment.