As Tommy already suggests it's a fake setup.
The keyboard shown is of a Kaypro 10 with the Kaypro Logo (and parts of the white frame) painted over. As an 1800 USD portable not exactly the 'core' of a '100,000 USD' system.
Graphics them self are clearly made up from a computer generated background and avartar, though the avatars scaling turning and movement are made with (back then) state of the art analogue film/TV tools as any rasterized graphics of that time would show scaling effects (jumps in size/pixel selection).
The graphics consist basically of three background images and two avatar (*1) hand drawn without any computer (*2) filmed (taped) and merged onto a single TV image by analogue means (*3) and filmed (taped) again. The text parts where done on a separate text based system (note the different angles used) as well as the 'final output' of the system.
In addition the graphics vary much between the 3 different shown 'video modes' to be a originated from a single machine of that time.
Game wise it's a mixup of several games popular at the time. This includes the series of (timeless) text only games of Infocom (Zork et al) of 1980ff, the text plus (static) graphics games of Sierra Entertainment of 1980ff and 'action based' dungeon games with directional/command key interface and graphics like the Wizardry and Ultima titles (both 1981 onward). All of them around 1983/84 at the height of their first boom.
The reasoning for such a mixup for a TV series is all about transporting the scene toward (less computer savy) viewers.
- Graphics are an easy way to 'show' what the game is doing.
- Supported by 'voice output' (in reality an actor and vocoder tricks)
- Spoken word can way better transport the intention/action Magnum is intending
Having Magnum muttering all along while just pressing some cryptic keys would make him look stupid, thus
- using classic text adventure commands and showing how 'he' types them will make him more of narrator voice than mumbling along.
So as usual when it comes to films, computers, games, and other software are tools to drive the story, not items in their own right - especially at a time when they were quite new and only used by a tiny minority.
Beside, I think it's well made, capturing the spirit of these games as well as the quirks of back then graphics.
*1 - One for walking straight and one toward the sides. Note how the avatar flips images when turning - after getting horizontal 'shortened'. It's the same image no matter if he walks left or right.
*2 - Note the fine details on the floor - quite hard for back then systems, even more so within the budget of a TV show. Similar the straight diagonal lines on his back.
*3 - Note the blurring when the avatar gets shortened when flipping - a hard to avoid side effect from using analogue circuits (at that time). Similar the black border of the character is a way to hide effects due source switching, which would otherwise be more prominent on horizontal borders and invisible on vertical.