The "qualifying date is 13 Aug 1914, that means that he landed in France on that date. To be eligible for the 1914 Star the soldier had to spend so many days in a "war zone" in that year. So they recorded when he arrived
The items in the stamped section are references to the actual entries for those medals, each one has its own book with more date - the card is just an index card pointing to where the "real" data is stored.
Any soldier who served overseas was entitled to the British Medal and Victory medal, The criteria were very loose, and literally millions qualified.
The 1914 Star appears to have been returned for adjustment - someone with more knowledge than I can tell you the exact bit of the Kings Regulations quoted. You may have to put your own post in the WW1 forum on Rootschat to find someone that can tell you.