Vulkan is already available, which removes any advantage that Windows might have had in the past beacuse of DX being ahead of OpenGL. VR related development in Vulkan drivers / Linux graphics stack is now active as well.

If you care about performance, you'd stay away from consoles anyway. They are way too limited in comparison.

So I don't agree that Linux is much behind technically. Smaller market share is more of an issue.

I've heard about vulkan for quite some time now, still haven't seen it used widely. Currently I do not see a future where Linux would be on equal footing with Windows when gaming is concerned. Linux would have to become way easier to use and have something that was strictly better than Windows. Free software and other ideological stuff won't make gamers to switch. What Linux needs is image and video editing suites to rival and surpass Photoshop, AfterEffects, Premiere, Final Cut, etc. Some streaming technology that is strictly better than anything available on Windows (so I guess OBS should drop Windows support or something) and then games would need to run at least on par. Maybe then some of the influential people (youtube personalities, twitch streamers) would switch over and bring their fans with them.

As long as Linux is just sort of viable there won't be wide adoption, because why would you change everything about your computing life for something that's +/-0% gain. Even at 10% better experience you might have to consider hard if changing over is worth the effort. Linux needs to magically become superior in many ways for people to hope on board in large numbers.

I have no idea how game development works, so would this mean that you can just compile Linux and Windows binaries from the same source code? Or is it just easier to make it multi platform? Also is there any thing like with Xbox vs Playstation were you have to do some platform specific tricks to get the performance up or is that way further in the line for optimisation?

It would allow using higher performance design where it's supported. Walled garden platforms like PS and Xbox will require duplicating the work anyway, thanks to MS and Sony being lock-in jerks in general. It wastes engine developers' efforts for no good reason, but there isn't anything they can do about it.