I feel the use of 'backdoor' here is misleading.
The software described would usually be classified as an Advanced Persistent Threat [1] or Rootkit [2] Backdoor [3] usually refers to methods to sidestep authentication added by the vendor.
1: https://en.wikipedia.org/wiki/Advanced_persistent_threat
2: https://en.wikipedia.org/wiki/Rootkit
3: https://en.wikipedia.org/wiki/Backdoor_(computing)