Good news everyone, I found a way to run the game. Here is the tutorial: https://www.youtube.com/watch?v=XRtqKEyk_ps
If you get message: Browser not supported, it means that you are either using 64-bit browser or you installed 64-bit Unity Web Player. You can solve this by using Internet Explorer 11 and installing Unity Web Player 5.3.8f1 32-bit.
Next you should get error: Update failed. No matter what version of Unity Web Player you use, you will always recive this error. Unity Web Player tries to update itself via server file Mono5.x.x-win32.zip. The file is either not present or access to it is denied. If you want some more information about the error, you can check log files in folder: C:\Users\\AppData\Local\Temp\Low\UnityWebPlayer\log.
To bypass this you will need to go to C:\Users\\AppData\LocalLow\Unity\WebPlayer create folders stable3.x.x and place inside files from versions 4.6.6f2 and 5.3.5f1. Its showed step by step how to do this in the tutorial.
 "Tauriel Teaches Typing"){kind=icon}
 "Transmission"){kind=icon}
 "Medieval Cop 8 -DeathWish- (Part 1)"){kind=icon}
 "Cursed Treasure 2"){kind=icon}