How to display edges in a 3D file on Facebook
3D graphics are not images they are instructions for images. Now the formats that export data beween systems work on lowest common denominator. Geometry is fine, but any effects on top of geometry would require you to agree on a set of instructions to implement. (no such reffort has been made for npr rendering lines).

The lines are not really part of the model that has been exported trough the gltf pipeline. Simply because the line rendering is a special feature of the sketchup system. There is no generic format that support those, since they need to be generated frame by frame. And there is 
quite possibly a infinite number of such features that could be implemented, none of these are part of the generally accepted set of things to export.

Most likely your out of luck the engine in question simply has no way to do this. So there is no solution for your problem. STL is a even more rudimentary format it only has triangles nothing else.

PS: This is why it is called an export not save. Although many applications have gone so far as to call even partial implementations save. But you can not just expect all things to go from application to application, especially in 3D