Living complexity?

Does "living complexity" mean "complexity of living organisms"?

Context:

It doesn't matter how many planets we have to play with, lucky
chance could never be enough to explain the lush diversity of
living complexity on Earth in the same way as we used it to explain
the existence of life here in the first place. The evolution of life
is a completely different case from the origin of life because,
to repeat, the origin of life was (or could have been) a unique
event which had to happen only once. The adaptive fit of species to
their separate environments, on the other hand, is millionfold, and
ongoing.