There are some libraries for different shields or sensors that have been written specifically for the Arduino board so they are based on their MCU architecture. Unfortunately these libraries won't compile on the Edison because its architecture is different. In some cases the library could be edited a little bit to make it compatible but in some cases it is not possible.
I have not tested the RFID shield you are using but I found another one that has been tested, please check the following document on page 38: Shield Testing Report. You will find a report for this shield and there is a note about the library used.
If you are not able to compile the library for you shield I would suggest you to write your own library. You can take the current Arduino library as a guide to write a new one.