This is a personal opinion. I do research related to the Systems Theory for long years, and it's clear for me that the alleged discipline of complex systems is just an academic fraud. Classifying a system as "complex" has a common cause: misunderstanding the classical Systems Theory, Epistemology and Philosophy.
I absolutely respect those who believe on it, but no debate has ever convinced me of the necessity of a "complexity" branch to the systems theory. The term complexity essentially means inability to understand, a feature that systems thinking is about; and systems thinking is a reduced pop subset of the Systems Theory, which already targets complexity. In fact, the classical Systems Theory was created to address complex problems, by splitting them into simpler ones (simple: easy to understand). A house system can be divided in multiple ways, but the proper division is that which responds better to a goal. For example, if my goal is to assign spaces to the members of my family, I can split the house system into room parts. That's the systemic way of solving the problem. etc. Removing complexity is what the Systems Theory is already about.
As you've found, there's not even a clear definition of this theory. Some associate the term "complex system" with classical systems (then, why is the name change necessary?), some associate it with some debatable features, allegedly not present in the classical theory, and in such case, either the features are part of it, they should be part of it without changing the name of the whole discipline, or they are (or should be) part of another discipline, commonly, biology.
The content of the "complex systems theory" is normally associated to biologic systems (Maturana et.al. target systemic features that should be part of biology, but without any rigor) or to classical systems (von Bertalanffy et.al).
... that a complex system is such that the behavior of the elements in the system do not yield wholly the behavior of the system as a whole
Association with non-linearity. Non-linearity is already a feature that the Systems Theory addresses, and it is a natural feature of systems (social organizations, for example; the central focus of the system theory). Non-linearity is common in nature, on non-living and living organizations. In addition: try finding a proper definition of systemic non-linearity. You fill, again, a lot of speculation based on subjectivity.
... in some sense the system is not predicted and may be thought of as something between total order and total chaos.
Chaos and emergence. The systemic evolution to chaos is simply described by thermodynamics, and the evolution towards order has no description ("complex systems" speculate about it, does not describe it). Naive ideas like emergence require more than speculation. For example, emergence is supposed to be the raise of new features, which are not present in the parts. Look this example: two dots. Alone they can describe two 0-dimensional sets. But together, in addition, they will describe a line. Wow. Emergence. And three dots can produce a plane. Loud wow. Emergence of a new feature, again. Is that excluded from the classical systems theory? No.
In addition, emergence describes a subjective perception. Life is a human subjective perception. And that is not mentioned in the "complex systems theory". The complex systems sellers should worry more about what is the content of the theory, instead of inflating superficial speculations. All the fuzz about emergence, non-linearity, self-organization ("self?" are those entities closed systems? closed systems are perfectly characterized by thermodynamics: no evolution towards order is possible in closed systems), spontaneous order (start defining order, in relation to thermodynamics, not as simple perceptions), cascading failures, openness (so, open systems are not addressed by the systems theory? what?), fuzzy boundaries (all physical systems have NO boundaries at all; all are open; on the contrary, ideal systems are essentially bounded), irregular transitions of state (a natural feature of systems), etc. should be part of some Theory of Biological Systems. The word "complex" is a very good seller, but not very scientific.
In addition, I tend to classify the Systems Theory in the category of metaphysics, as Kant classifies Arithmetic and Geometry (well, properly, Mathematics). Like numbers, systems are bounded ideals, not material things. Matter has no boundaries. There is no spoon out there.
I Repeat: this is a personal opinion.