I believe the running theory has been that it's a defense against Microsoft being Microsoft. If MS tries to do something like force all NT apps through their own store and take a cut of every sale, or anything else that poses too much threat to Valve, then Valve has an escape hatch in the form of Linux support. "You want 30% of our sales? Screw you, we'll tell our users to switch to Linux!" is a bit extreme, but it just needs to be a deterrent.
There is no fundamental reason why it can't eventually take over gaming, or even desktop.
The kernel used by Android is completly irrelevant to userspace and can be changed tomorrow at Google's will, and only OEMs and rooted devices will actually notice it.
On embedded there are plenty of OSes to choose from, with FOSS embedded industry support moving to MIT/BSD licensed kernels, as OEMs don't want to deal with shipping GPL code on embedded devices, specially after v3 happened.
One thing I'm observing is that macOS and Windows are basically regressing to have the same type of nonsense and quality issues that are indeed typical on desktop Linux. It's possible (but not certain) that they'll eventually cross paths. Linux might not take over the consumer desktop market (unless it's under a proprietary shell, like Android / ChromeOS), but Linux could possibly take over the high-end/power user/workstation market.
And yes, seriously, _thank you_ Valve!