This web site talks about building c++ executables for Linux from visual studio.
Can this approach be applied to Intel Fortran to build for Linux from VS?
Unlikely - I am fairly sure that extension relies on the VC build system, which Intel Fortran does not use. Do keep in mind that the extension is just using Visual Studio to kick off builds on a remote Linux system.
I've had success porting Fortran developed in VS for Windows to build on Linux by using a makefile on Linux. My approach is to copy the Fortran files to the Linux computer, then run the makefile to build there (mostly build shared object .so libraries). I don't make any changes to the Fortran on Linux, just build and run there so that I can do my development on Windows in VS. As a test I also build on Windows using the "nmake" utility with a Windows format make file. Is building on Linux using a makefile your approach too?