The test results you have selected are very old and may not represent the current state of Wine.
Selected Test Results (selected in 'Test Results' table below)
The installer works fine at installing the game. The title screen appears with music.
What does not
After the Kingpin Title Intro has completed, the program halts with a "Hardware Not Detected!" error window.
On a Windows machine, you would get this message if you never installed your graphics drivers for your video card. I had ATI catalyst drivers installed and working on my Linux test machine, and I still got this error. Judging by the debug messages, it looks like a glide dll is not available.
err:module:import_dll Library glide2x.dll (which is needed by L"C:\\Program Files\\Kingpin\\3dfxgl.dll") not found
What was not tested
The rest of the game unfortunately.
There is a Linux installer for this game, but I couldn't get it to work.