Even though it was not very popular in the US, the Atari ST computer line was hugely successful in Europe. Not only it was a good game and graphics machine, in some respects rivaling the Amiga, its built-in MIDI support made it the system of choice of every musician and record producer back then.
Alpha Waves / Continuum
Perhaps the first fully 3D platformer ever, and one of the first fully 3D games of any kind on a home system. Very abstract (unavoidable with the technology at the time), you have to bounce around 256 rooms and collect tokens under a time limit. It's easy to see this was the likely inspiration to Geograph Seal and Jumping Flash.
Capstone to the Wizardry/ Bard's Tale type of first-person dungeon crawlers. Combat is timed instead of waiting for everyone to have a turn, so you can run away and monsters can sneak up behind you. Pick a party of up to four pre-gen characters by walking through a gallery, click on the screen to push buttons and throw weapons, drag-and-drop inventory, cast spells one syllable at a time. Roguelike in you start over if you die, but dungeon isn't random so you will remember where traps are. These days there are speed-run competitions.
Attention, shootan fans, this is a true historical landmark: the very first arena FPS of all time (in the modern sense of how the genre is defined). And did you think those MIDI ports were just for music keyboards? No, they used it to network up to 16 machines. Very, very impressive for a 1987 game. Also released for other systems later as "Faceball 2000".
Sundog: Frozen Legacy
Space trucking to earn money for upgrades and fuel, to find the three macguffins to complete your quest. Operating your spaceship means moving from workstation to workstation for the interfaces. The main game is elite-like star-trekking, but you walk around on foot after you land for some exploring.