Imagine an "acronym" but instead of taking the first letter of each word, you took the entire first syllable of each word. I notice Japan, which incidentally has a syllabary, seems to create this sort of "acronym" fairly often.

Is there a word, like a linguistics word, for this type of syllabic "acronym"?

The word for that is "acronym." The one where the rule is to use only the first letter of each word is an "initialism" although it's usually considered as one type of acronym.