Hi,
I, once again, installed Far Cry 2 on my newly built PC.
I tryied to launch it. Got greeted by familiar splash screen then black screen and exit to desktop.
So, I started my quest to make it work again.

My system:
Windows 10 64-bit 1909 18363.778
Ryzen 7 2700 - 8 cores 16 threads
16GB RAM
GTX 1060 6GB
Newest chipset and graphics drivers (445.87)

I ran around Google and found no fixes to my issue.
It really puzzled me and found solution.

1. Go to your installation folder
2. Navigate to "bin" folder
3. Right click on "farcry2.exe" and select "Properties"
4. On the "Compatibility" tab check "Compatibility mode" and select "Windows 98 / Windows Me" in dropdown menu
5. Click "OK" and enjoy!

Why did this help?
Maybe the game´s engine got confused what hardware do you have and crashed, because it did not found appropriate hardware setting. By using compatibility mode for super old OS, the engine falls back to the lowest setting at least.

Limitations:
Do not use "Optimal" video setting. The game is confused and does not provide correct settings for "Optimal" mode. Instead use the "Low" to "Ultra" settings.
The splash screen is not available. Instead the game will seem stuck at taskbar and after a while it launches.

Recommendations:
Do not ever use DirectX 10 mode. The game has many known bugs when using it.

I am making this thread to notify you about this solution as no one posted it anywhere.