I just today compiled a version of my game, Riders of Asgard, for Linux and released it. I also do a Windows Cross-Compile build and it worked as well. As @Gwenn states, in order to get the editor working on Linux, you have to build it … Epic does not release a native binary on Linux for the editor.
It is quite simple to build it on Linux and I have done it several times.
The launcher doesn’t work on Linux and that is primarily what the problem is, I overcome this by adding the assets I need to my project on Windows and opening it in Linux … it is a workaround but one that works.
Personally I don’t actually develop in Linux, but that is mainly because most of my pipeline and workflow is based on Windows tools.