I've tried a few of the basics running in compatibility mode and administrator, unfortunately, those don't work and there isn't a lot online about fixing this thing.

According to this thread it should be possible to run the game through DxWnd. Unfortunately I don't know how that emulator works as I never used it before.

Using dgVoodoo also works ingame (gameplay & ghost cutscenes) but the intro and ending cutscenes will be completely broken.

installing nGlider and running Goglauncher.exe worked for me

I managed to make the game run with DxWnd. All cutscenes that gave me trouble before are now working fine.

https://sourceforge.net/p/dxwnd/discussion/general/thread/6a89ebe6/

Download the latest version of DxWnd and also download the KTnew.dxw that you can find on the link above.

Installation

• extract all the DxWnd files into a folder
• put the KTnew.dxw file into the exports folder
• open DxWnd and click on File and then Import
• import the new KTnew.dxw file
• right click on the KT symbol and chose modify
• in the main tab make sure that "Run in Window" is selected or else the game will crash when the intro starts
• select also "Hide desktop background", "Keep aspect ratio" and "Desktop center"
• Path and Launch must lead to the folder that has the KILLTIME.EXE included
• put your resolution in W and H (1440x1080 for example)
• switch to the video tab and select "modal" for Window style (will make the window borderless)
• change "Screen resolution" to HDMI or Native
• switch to the Mouse tab and select "Hide" for Cursor visibility
• click on the OK button and then on File and Save to save the config
• double click on the KT icon and wait until you see the DxWnd logo appear (don't move your mouse while the game is loading or you will have a black screen for some reason!)
• play the game and have fun

Oh one more thing. If you don't want mouse movement (forward & backwards) use this: https://www.gog.com/forum/killing_time/how_do_you_make_the_mouse_not_move_the_character/post4

You won't be able to circle strafe in this game but at least you can use WASD for movement and the mouse for turning left and right. Better than the default controls by far.

but thats also still crap.
gog is selling a game that doesnt run well and those who bought that game have to look for themselves, to get it running.
that is not acceptable in my opinion.

Not GOGs fault. They haven't programmed the game. Blame the lazy devs who don't patch it. At least there is a method to make it run well without any major problems. GOGs version is still the best one available as it won't kill EXPLORER.EXE every time you run the game. The Steam and Zoom Platform versions do that.

Mine runs fine on 2 separate machines, win 7 and 10, respectively; intel hd and radeon ones also so... go figure. Still that's a pain to run this game if I remember well.
Will try on a third machine, windows 7 (8gb ram/nvidia 8600m) and see how it goes.