From my mind, gameinstance is instantiated for each player on player’s side (if you are in mode server + clients, there is one more gameinstance on server side).
Their information are not shared, and are local to your player.
You can find very good information on which class are shared or not in this document:
http://cedric.bnslv.de/Downloads/UE4_Network_Compendium_by_Cedric_eXi_Neukirchen.pdf