Kinetic synesthesia evoked by abstract thoughts? Can the experience of movement when mentally visualizing the network/structure of the code of a complex application, and the information that flows through the network as a programmer be a kind of synesthesia experience, or is there something else at play? Movement akin to being drawn in different directions or tilting forward, as a result of experiencing the structure.
Short answer
No.

Background
The definition of synesthesia is generally as follows:


  ... a perceptual condition of mixed sensations: a stimulus in one sensory modality (e.g., hearing) involuntarily elicits a sensation/experience in another modality (e.g. vision). Likewise, perception of a form (e.g., a letter) may induce an unusual perception in the same modality (e.g. a color).


The most common form of synesthesia is thought to be colored hearing: sounds, music or voices seen as colors. Most synesthetes report that they see such sounds internally, in "the mind's eye." Only a minority see visions as if projected outside the body, usually within arm's reach (source: APA).

Most of the discussions I've had with peers in that field reported to work with people that see letters and numbers to have a particular color. Indeed WebMD reports that


  One of the most common responses [of synesthetes] is to see letters, numbers, or sounds as colors.


Hence, I think that synesthesia often (but see the APA site) manifests itself through relatively 'simple' visuals brought about by relatively 'simple' stimuli. The number '4' appears to be green etc. In contrast, the highly cognitive complex associations you are envisioning seem unlikely to occur. Further, synesthesia is mostly coupled to the senses of vision and hearing, and not to motor functions. So, to answer your question, no I don't think so.