I disagree with the entire list. There is not one single form of "ammo" on it. Those are all "calibers."
Ammo, refers to ammunition. This list should be more along the lines of:
Varmints:
1) VMAX
2) TNT
HM) HP
Medium Game:
1) Sierra Game King
2) Nosler Partition
HM) BT
Well you are right about his choices being cartridges and not ammo.However your choices are all bullets and not ammo either.