Is it animal cruelty if someone killed the animal and didn't eat it?

Personally, I think it's animal cruelty either way unless it's for some necessary purpose like pest control or medical testing.

its an unnecessary kill unless its an over population problem

Depends on the circumstance . Vermin and dangerous predators get shot on sight ... game animal have regs ... you have to process the carcass

Remember that the next time you set a rat trap.