He lets Zombie John Connor live.
Zombies present no threat to Skynet - they are far more interested in the pursuit of brains than toppling the oppressive boot heel of their mechanical overlords and returning the earth to its rightful human owners - but an incredible threat to the remaining human population. Letting him infect and accelerate the destruction of mankind would be in the machine's best interest.
That's funny that you said "He lets Zombie John Connor live
Actually, a zombified John Connor would be a Skynet plot. Kill him, reanimate him, send him back to base, let him infect others. The human race would end up wiping themselves out.
We'll call that movie Terminator: Day of the Dead.