While it is an Atari that was used. Don't consider a writer using it out of the ordinary or abnormal. Many folks used Ataris.
Atari- both the 800, xl, xe line and ST (and E) were used heavily in music in that era. Atari also made specific hardware for cinematic work and production. Sound and Graphics solutions. Much of it tossed, lost, or buried in with piles of props now.
I don't understand your assertion. This was purely a writing purpose, not cinematic, production, sound nor graphics. The first is more than a iconic movie, it still is a pop cultural phenomena. The writing was a very big part of that success.
I've never heard of a prominent or famous movie script or book written on an A8. Many writers were not even tech savvy back then. The printer in the photo is a HP Laserjet II, introduced in March of '87. So he was writing the BTTF sequels on A8 as well!! That's highly unusual and notable. Most computer users in '87 in this country were dreaming of upgrading to a 16bit machine (or a faster PC) if they hadn't already.
IMO in the late 80's A8 was approaching rare status as a daily driver in the USA, let alone a work computer. PC's, C64's, Apple's etc were common yes... It's a safe assumption most writers didn't even use computers at home in the early 80's.
The other thread here mentions this paragraph:
Bob Gale got his first computer in 1980, which was an Atari 800 hooked up to a black and white television, one of the only home computers you could buy at the time, other than a Radio Shack TRS 80, nicknamed the "Trash 80."
I like that he stuck with the platform for years. It worked for him, apparently. He was an early adopter and loved his Atari 8bits.