A usual problem when compiling programs on Windows is that GUI executables cannot write to the command line from which they are started. To do that you have to compile them as Console executables, but then there is always an annoying command line window poping up when running it from a shortcut.
The solution is to ship two executables, one compiled as GUI, one as Console, and that is what Eagle is doing. The GUI executable is eagle.exe, and the Console executable is eaglecon.exe.
An informal convention when using that dual executable solution is to use the same base name for the two files, but using the .com extension for the Console executable. This has the advantage that you only have a single name to document and remember ("eagle"), but thanks to the default order of extensions in the Pathext environment variables, eagle.com has priority over eagle.exe when run from a command line (and one can still explicitly run the GUI version by typing "eagle.exe"). In shortcuts the full path to the .exe is necessary anyway, so it's not a problem to have a "conflicting" .com file. This convention is used for example by the Microsoft Visual Studio IDE (devenv.exe for shortcuts, devenv.com for command line use and scripting), or the Inkscape open source vector graphics editor (inkscape.exe for shortcuts, inkscape.com for command line use and scripting).
My suggestion is then to simply rename the file "eaglecon.exe" to "eagle.com".
