Does Laserweb also work with an Eding CNC Card?
No, those cards are for LinuxCNC or Mach.
Edingcnc is a series of high quality motion controllers which is only compatible with their proprietary CNC software. From what I have read, they are very good and reliable. Laserweb4 cannot directly communicate with the controller cards however you can still generate gcode with Laserweb4 and save the file. The Edingcnc software is gcode compatible and should load/run Laserweb4 gcode files.