The label "Systemic" is related to the System Networks used in the description of the Lexicogrammar of human languages. A system is a theorical tool to describe the sets of options we have in language and the progressive refinement of these options in sub-options. It is similar to a menu-directed interface in computer engineering for it is a one way refining model that can be mapped by a bipartite directed graph in which the A nodes are labeled features and the B nodes are labeled gates or systems depending on their cardinality. Every system and gate have one single feature as their entry condition and one feature can be the entry condition to any number of gates and systems.
The main issue on using Systems to describe language is that by using them we assume there will be no cross-cutting refinements of any kind. In other words, two different systems cannot meet together and be partially refined as one system. This phenomenon is supposed to happen as one refines options on and on. By using Systems, it is possible to describe language up to a certain refinement (and this may vary according to the theorical compromises one makes), but not further.