Not sure about the machine but according to Romero[1] Quake (as with Doom) was developed on NeXTSTEP 3.3, which they continued to use, later running on Intel hardware, until 1996.
Would that have been running NT back then, perhaps the MIPS version?
The environment does look like Visual C of which 1.0 came out somewhere in the 94-95 time-frame if I'm remembering it correctly, though it might have been just a tad earlier.
I bought one of these machines around that time for a design company I was interning at. It's an Intergraph, obviously I have no idea which model. These machines were built to order, so it could have anything in there. That multimedia keyboard brings back memories, prolly the worst $100 I ever spent.
This machine would be running WinNT 3 or 4, most definitely not the MIPS build.
QuakeEd on NeXTSTEP: http://rome.ro/uploaded_images/qe_dev-726646.gif
[1] http://rome.ro/2006/12/apple-next-merger-birthday.html