Steve,
according to the Verordnung from the 2nd September 1903:
"
... that the badge is only awarded every two years and that it is only to be worn by the MG-Abteilung for one year. ..."
... so I assume that the entire MG Abteilung received the badge!???
In the "Taschenbuch des Generalstabsoffiziers" from 1914 it says about MG-Abteilung:
4 officers, 112 NCO's, enlisted men and lower officers.
So there were probably a maximum of 112 badges
(in the army corps every two years)?
Just a guess, unfortunately there is nothing about the exact number.
Best regards, Jens
Pietsch Königs-/Kaiser-Abzeichen
Addition:
for the navy I think that only the gun crews received the badge:
"... Das Abzeichen erhalten sämtliche Mannschaften, welche bei der Verleihung des Kaiserpreises zur Geschützbedienung des betreffenden Schiffes gehört haben und sich an Bord befinden. .."