Apparently as early as May 1987 the term minicomputer
was used in the WHITE HOUSE executive offices and quoted in several newspapers, along the
lines, "Without a minicomputer one really can't tell ..."
Given the lack of technical expertise in Washington, this suggests a much earlier origin
of the word.
I searched on
www.newspaperarchive.com a few minutes ago and saw that
same article, along with a couple of others from 1967. But in most
cases it's written as "mini-computer". That hyphen may make a
difference. It could be newspaper editors simply deciding to hyphenate
a then-unfamiliar word, or, it could be that whoever said the original
quote meant it as, "Without a miniature computer," while having zero
knowledge that something technically called a "minicomputer" was being born.