Last Starfighter was assuredly NOT done on an Amiga, nor anything remotely resembling a desktop system. All the CG was done by John Whitney Sr.'s company, Digital Productions, on a Cray X-MP supercomputer.
DP was eventually bought out and merged with Robert Able productions, another early pioneering CG company.
I've worked with a number of folks who were on this. It's a respected and loved film, both for its cinematic and technological achievements. The effects look deeply dated today, but at the time, they were mind-blowing. There's even an industry joke about it:
How do you know you've been doing computer graphics for too long?
You can remember sitting alone in a theater watching 'The Last Starfighter' and thinking "Wow. This is even cooler than Tron!"