Caliber laws are for hunting, a minimum is set for humane hunting.
It is to reduce inhumane wounding and animal suffering from inadequate calibers.
Some hunters would use rounds that could just barely take an animal, or only take an animal at a certain angle with excellent shot placement, and not achieving near perfect shot placement leave live animals to suffer, or die of their wounds or infection hours or days later.
A minimum helps to offset this possibility and give some margin of error in shot placement. Where a good but less than perfect shot will still humanely take the animal.
Self defense is self defense and the caliber does not matter legally. If it was determined to not be self defense and you did not have the proper hunting license or tags it would be illegal poaching.
If it was determined to be illegal poaching I don't know if they would be able to add an additional charge or enhancement because the caliber was also illegal to hunt with.