Based on my observations, the skills are solely transferable in same genre of games. I've seen great FPS players switching to different titles. I have never seen a great FPS player doing well in RTS and opposite.
Is there a whole host of ex e-sports players making a professional living off poker? Or are these guys outliers?
The odds of someone waking up some day in a world where competitive FPS ESports have vanished is probably roughly comparable to the odds that someone wakes up in a world where competitive hockey has vanished -- that is to say, unlikely enough that's it doesn't seem to be worth worrying about.
The future might be AR/VR games. If you spent your whole life using keyboard and a mouse, you're gonna have to get used to the new interface.
I think the teamplay and drive many of those players have is transferable. You have to let the video game run your life, like any other sporting professional. The mouse movement, keyboard habits and reaction speed are also all mostly transferable. At the end of the day I think its mostly determination to switch and time.
So, it does happen, but you’re right in that the skills are not easily transferable. The only thing that is, is your dexterity.