It would require that a Linux based OS was released which allows games companies, in a standardised way, to take full control over the system. And at this point, it won't be a Linux distro, it will instead just be like Android. I think calling that a market takeover would be similarly thin and insignificant as calling android a "Linux takeover of the mobile OS market".
But this isn't to say that Microsoft won't lose the market share to "Gamedroid" or whatever, it just won't be losing it to Linux.
* As has been demonstrated, KLA and similar technologies do help make cheating more difficult and require more resources. But, as the cheating industry's pocketbooks make clear, cheating hasn't stopped, it has just become more discreet such that most players simply don't notice when they're losing to cheaters.