The Terminator was developed and published by Bethesda Softworks in 1990. I have not been able to get this to work in Dosbox, but will upload an in game shot when I get around to running it on a Dos PC.
The game was a combination of FPS and arcade action in cars plus some sideways scrolling action. Given it's FPS element it should probably share the accolade with Corporation as the first FPS for the PC.
I have a boxed copy and it came on 5 1/4 inch disk.