The game instagrammers play in order to gain more followers/likes. Common tactics include following your prey until they follow you back and then promptly unfollowing them or using hashtags such as #follow4follow and #like4like. Another example would be asking someone to follow you and then not following them back after they have followed you.
Taras: "Hey Tim, I got Carolyn to follow me."
Tim: "Careful she doesn't instagame you. Shes a beezy."
Taras: "Tim, I lost a follower!"
Tim: "Dat Instagame doe."