Chrome and Safari for the longest time used the same rendering engine WebKit, until a couple years ago when Google switched to Blink. So it wasn't hard for Google to roll out a version for iOS utilizing WebKit to comply with App Store rules seeing that Blink is a forked version of WebKit. The same cannot be said about Chrome on Windows 10S. I'm not saying its impossible, I'm just saying its improbable as it would require a lot more time and investment from Google where I'm not too sure they're that interested as Windows 10S directly competes with Google's Chromebook ambitions
But globally the chromeOS is about as popular in the PC market as windows 10 mobile is in the smartphone market.
Google is a search company, they make no money from chromeOS. They only make it indirectly from search. Same with android.
If windows s, with its bing default search engine makes any real headway, that's the real threat to their margins. Same reason why MS makes smartphone software for android, and google makes google assistant now for iOS, google will want to keep a presence in windows 10.
With MS increasingly doggedly pursuing UWP, truly bullish and determined as they should be, its really only a matter of when. When enough of the PC market gets their apps from the store, google will want to be there, to keep their search revenue.
Possible windows s won't do it. Although personally if I were google I'd do it. Windows has more global mindshare in desktop/notebook, more of a bulwark in education - so windows s has a good chance of success especially as opposed to chrome, which faces the same growth limitations as a range of other US only stories AND no one can afford to lose young minds.
And they later they leave getting into the store, the more they risk losing search revenue/google search customers, their primary income stream.
Basically all they do by delaying this as long as possible, is give MS a chance to catch up in the search game. It is after all still right now, a higher search market share, than chromeOS has pc OS marketshare, or windows 10 mobile has mobile marketshare OR even windows tablets have tablet marketshare - bing is a genuine threat. Windows, not so much (most windows users do use google).
So the threats there are - default search engine, default browser and AI assistant. Which is entirely featured in "s".