This looks a bit old, but this person apparently successfully ported the real Space Invaders arcade game to a TRS-80 Model 4/4P with hi-res board (the board being the x-factor here and something few of us with TRS-80 collections have (I don't)).
Pretty extraordinary stuff and as the author says, probably the first of its kind ever attempted. As we know, someone did something similar on the far more capable (though no less impressive of a technical achievement) TRS-80 Color Computer 3 with arcade Donkey Kong.
Keep in mind that the Model 4 came out in 1983, based off of a platform first released in 1977, and the Color Computer 3 came out in 1987, based off of a platform first released in 1980!
Thanks to the work of some gentlemen here, I was able to compile my own version of games that work best with a 4-way limit joystick under MAME. All-time personal favorites Pooyan (really a 2-way) and Satan's Hollow are of course on there...
Here's the list of 208 matches, with each game hopefully only listed once (anything missing or corrections? Let me know!):