I have done some more digging, and it was DEFINITELY from Final Fantasy Online. I found the webarchive entries for the site, and the video was available until July/August 2000 when all movies were removed from the site due to bandwidth issues. The file was described as 'Official Final Fantasy Online site trailer' and had the filename ffonline.mpeg (I actually remember this now, as I was on dial-up at the time and it took AGES to download). You can see the webarchive entry for the page here:
http://web.archive.org/web/199910120...ff8-movies.htm
I have posted on Final Fantasy Online's forums, but no-one so far has a copy. I have emailed Final Fantasy Online's staff, and have had no reply yet.
The footage was only from FF8, and I am 99% sure it was only FMV footage. The video must only have been available for a few months, so I feel lucky at having seen it anyway... but surely someone must have a copy out there?
The only other detail I can give is that the orchestral music built up and built up and hit a massive crescendo... then the website address faded in... black screen, with the name of the site across the middle, with a moogle stood leaning against the logo. While this happened the music became very soft, and choral... I could even whistle the music from this video, it was so memorable
I would LOVE to get a copy of the video, and would love to find out what the music was
