For a Latin-language artificial intelligence called Mensa Latina the user manual will need to discuss and therefore refer to the phenomenon in Latin prose where meaning comes from grammar and inflections more than from syntax or word-order. But what is the name of that process of scattering words all about in a seemingly random word-order?
If Latin prose had an "extremely loose word order", which is (generally) not the case, the appropriate linguistic term involved would be "non-configurationality". However, rather than being vaguely classified as a free word order language or as a non-configurational language, Latin has been referred to in the recent literature on Latin syntax as a "discourse configurational language" (cf. the references by Devine & Stephens (2006, 2019) and Danckaert (2017) below). Latin word order has been claimed to be strongly driven by so-called "information structure" (involving notions like "focus", "topic", etc: cf. https://en.wikipedia.org/wiki/Information_structure ).
NB: a key expression in Mentifex's question is "seemingly random", whereas a key word in Draconis's answer is "understandable". The former expression is to be related to the fact that, despite appearances, Latin is not a free word order language, whereas the latter expression ("understandable") is to be related to the fact that word order in Latin prose is determined by pragmatics (by information structure. E.g., see the authoritative works by Devine & Stephens (2006, 2019) and also the impressive work by Danckaert (2017) below).
Following a suggestion made by Draconis, I add the following quote by Jules Marouzeau (1949: 191), which nicely summarizes his/her answer: "l’ordre des mots en latin est libre, il n’est pas indifférent" (‘Word order in Latin is free, it is not arbitrary').
Marouzeau, J. (1949). L'ordre des mots dans la phrase latine. III. Les articulations de l'énoncé. Paris: Belles Lettres.
Four more recent references on the topic are the following ones (NB: it is a personal selection, of course. As you can imagine, there are many more works, since word order is a (the?) constant hot topic of Latin syntax). There seems to be a consensus among generative and functional approaches (e.g., cf. Danckaert and Devine-Stephens, on the one hand, and Spevak, on the other) on the relevant role of pragmatics and information structure. Cf. the important role given to stylistics in the excellent traditional work by Marouzeau.
Danckaert, Lieven (2017). The Development of Latin Clause Structure: A Study of the Extended Verb Phrase. Oxford: Oxford University Press.
Devine, Andrew M. & Laurence D. Stephens (2006). Latin Word Order. Structured Meaning and Information. New York: Oxford University Press.
Devine, Andrew M. & Laurence D. Stephens (2019). Pragmatics for Latin. From Syntax to Information Structure. New York: Oxford University Press.
Spevak, Olga (2010). Constituent Order in Classical Latin Prose. Amsterdam/Philadelphia: John Benjamins.
Caveat: these monographic books are perhaps mainly useful for the latinist and for the linguist interested in Latin. If you are more interested in the topic from a more basic/simpler/didactic perspective, I recommend you the reading of chap. 18 "Word Order" from the very useful textbook Latin Grammar by the late Dr. Dirk Panhuis, who, by the way, was an expert on the topic of Latin word order (NB: he wrote a doctoral dissertation on this topic from a functionalist/communicative perspective). Cf. a brief review of his excellent Latin Grammar (one of my favorite textbooks) in: http://bmcr.brynmawr.edu/2007/2007-08-49.html