The reference to "similar state lands" was removed from the final rule. It was thought to be confusing and ambiguous at best. Obviously, a smart move.
As long as you have a CHP issued from the state
in which the National Park or refuge is located, you may CC. You may also CC in National Parks and refuges located in other states so long as that state accepts your "home state" CHP through reciprocity or other similar recognition.
Note that you still can't CC in federal facilities/buildings. This includes visitor centers located in National Parks and refuges.