It's a free wrapper for old graphics API's made predominantly for W7/8/10 OS, also works with games and will help you to get the game working.
You can get dgVoodoo 2 from this website[dege.freeweb.hu]. Some users say that only several specific versions of dgVoodoo are fully compatible with JKDF2, but the latest worked fine for me, so you can look for the latest version too. Move to downloads page and look a little lower to find the latest version (currently it's 2.54).
After download, you will see the similar content of the zip archive:

Extract everything except html files (which are not needed) and launch dgVoodooCpl.exe. And this is what you will see:

To be pretty sure I did some changes in General tab. For Output API choose feature level 10.1, as it should be most optimal to run the game with less issues. For Adapter choose your primary graphics card (for laptops choose the external adapter as it provides better performance). In Full Screen Output list you will see the only display to choose (I'm not sure about multi-screen users).











Now switch to DirectX tab. You will see this:
There's no actually any option to be adjusted, but at the end make sure that Disable and passthru to real DirectX is UNCHECKED.
Hit OK and close the setup. Now let's get to the next step.

Go in to the MS folder inside the dgVoodoo 2. You will see three .dll files. We need two of them, these are D3Dlmm and DDraw. Copy them and head to the game's folder located in Steam Library. The path should look like:
C:\Program Files (x86)\Steam\steamapps\common\Star Wars Jedi Knight (for x64 users, otherwise you can see only Program Files folder in system volume).
Paste copied files into game's folder along with .exe files. Then backup or completely remove Jedi.EXE as it prevents the game to launch.
To be sure here are the screenshots how the game's folder should look before the changes ana after them.

Before:


After:

As you can see I did not delete Jedi.EXE file, however it's not necessary, at least it should be not called .exe.

That's it, nothing is left to do. Let's start the game.

Before starting the campaign make sure that 3D Acceleration is Enabled.
Now the game should run perfectly.

I have read other many guides from the Internet which also promised to fix the game on Windows 10, but they didn't help me, and the compatibility mode made some troubles for me... I hope these methods were quite clear and helped you to run the game without any problem.
Also, these methods work with the Mysteries of the Sith DLC. You can see the instructions here:
http://steamproxy.com/sharedfiles/filedetails/?id=803936253
If you need additional help, leave a comment or contact me personally. Will be glad to speak with you all :)

6/28/2017:

• dgVoodoo2 has been updated to 2.54
  
• dgVoodoo2's .exe file is now dgVoodooCpl.exe instead of dgVoodooSetup.exe
  
• Since Backbuffer in System Memory does not impact to game's performance and gameplay, this text was removed
  
• Pictures updated according to new dgVoodoo2 version
  
• Minor text corrections