I'm going to run it and have a look in a bit and get back to you.
It looks like 1st Word on the Atari ST also have a continuous spell checker.
https://en.wikipedia.org/wiki/1st_Word
From the link for 1st Word :
"Among the many new features was a spell checker with a 40,000 word dictionary, although lacking many American English terms,[11] a mail merge program, footnotes and semi-automated hyphenation.[12] The spell checker included the relatively rare, for the time, option to check on-the-fly. It also added document statistics display, including the number of characters, pages, etc"
Honestly I'd guess it's one of those things that possibly originated at Xerox Parc and then got added to consumer products from the 1980s onwards.
Personally, I remember it because I remember seeing Word 6 and thinking 'at last they have caught up to Prowrite'.