Let's assume that on the plate you see "Blue screen". It was the last drop of impatience I loosed. After that I permanently moved to GNU/Linux
Depends on what tools you are going to use. If you want to use something really portable for example godot, it can make sense to export it for windows also. If you want to use for example sdl/c++ it would be pain to compile it for windows without windows.
Do you want something that really exclusive for linux? Something that can be compiled only for linux? It shouldn't compile for windows even if you have source code? It is a bed idea.... Anyway you can create your game as part of linux kernel. You can use POSIX API.... It will make you game bounded to linux and make it is more hard to compile/run it on windows but I don't recommend you to do it if the goal is just to create this bound just because you want this bound...
In general I always recommend godot.