A Multitasking GUI, Circa 1982
autospa points out a post (with video) showing off the multi-tasking abilities of the Blit terminal, developed in 1982 by Rob Pike and Bart Locanthi. Before Windows, before X, and before the Mac (but somewhat later than the Xerox Alto), the Blit terminal provided a multitasking, mouse-driven graphical interface; it took a Unix server on the other side to do the heavy lifting, though.
In 1985 the Amiga brought "real" multitasking to the home computer using masses, many years before it was available in Windows or Mac environments.
Of course multitasking was around long before that, but I think the Amiga 1000 is what made it available to Joe Sixpack, who wasn't going to be using heavy duty Unix workstations or what ever.
[The Atari ST's TOS/GEM] wasn't useless and did multitask. True it was via special applications referred to as 'accessories'. However, if you used a wedge you could stick any application in as an accessory and as long as it didn't need to write to the screen to keep running while back grounded, it worked rather well..
Let's put this in context. That somewhat stretched, certainly limited and somewhat kludgey version of "multitasking" might sound passable compared to MS-DOS-based PCs of the same era. Not that big a feat given that mid-80s PCs were running MS-DOS, an early-1980s ripoff, er.... *port* of the 1970s 8-bit-microcomputer-era OS CP/M.
However, the ST's main rival, the Commodore Amiga (which hit the streets at almost exactly the same time as the ST- mid-1985, and not 1984 as you state) featured full pre-emptive multitasking as a standard part of the operating system. No silly restrictions or workarounds for what was basically a single-tasking OS required, because multitasking was an integral part of the OS. You simply ran two or more programs at once and they worked- period.
And this was "proper" pre-emptive multitasking, not the more primitive co-operative multitasking (which relied on well-written programs yielding control themselves) that even Windows 3.x was still using in the early 1990s.
Thing is that although the Amiga was generally a more advanced computer than the ST, it had the same basic CPU- the 68000- running at similar (actually, slightly slower) speed- and to the best of my knowledge its multitasking (and other aspects of the OS) weren't reliant on the Amiga's custom hardware. So I'm pretty sure the 68000-based STs *could* have run a more advanced multitasking OS in theory, even a port of the one that the Amiga had(?!)
But the fact was that they didn't, at least not back then, and the "multitasking" you describe was at best a restricted hack that clearly *wasn't* the best that could be done at the time.