That software doesn't contain a backdoor, but the fact that a new software load could be created and installed could be viewed as the backdoor itself. But if that software doesn't currently exist, is the mere potential of it a backdoor? Somewhat of a philosophical question.
If Apple prevails and doesn't write the software the FBI is demanding, then the backdoor is not there.
The later iPhones with the Secure Enclave may truly be unbreakable if they protect their secrets with hardware in the chip.
But my understanding of it is that Apple is NOT capable of unlocking the phone right now. The FBI is demanding that they develop that capability. So I guess they're capable of being capable...
† At the risk of being an armchair SE expert...