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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?

I've always heard it described as free word order. That is, the word order is "free" in that it can be pushed and pulled and twisted every which way while still being understandable.

If Latin prose had an "extremely loose word order", which is (generally) not the case, the appropriate linguistic term involved would be "non-configurationality" (e.g., cf. https://en.wikipedia.org/wiki/Non-configurational_language ). However, rather than being vaguely classified as a free word order language or as a non-configurational language, Latin has often been referred to in the recent Latin linguistics literature as a "discourse configurational language". Latin word order is strongly driven by so-called "information structure" (involving notions like "old information", "new information", "focus", "emphasis", etc).

NB: the key word/expression in Mentifex's question is "seemingly random", whereas the 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 (unlike Latin, the Australian language Warlpiri, for example, is a non-configurational language), whereas the latter expression ("understandable") is to be related to the fact that word order in Latin prose is clearly determined by pragmatics (stricto sensu, by information structure. For a very recent reference on this topic, please take a look at https://global.oup.com/academic/product/pragmatics-for-latin-9780190939472?cc=es&lang=en&# ).