Chinese Whispers is a game which a group of people play. Player 1 whispers something to Player 2 and 2 to 3 and so on around the company. The idea is to see how distorted the original message is once it gets back to its starting-point.
One of the most famous was reputedly the military one which started as: "Send reinforcements; we're going to advance" which eventually became: "Send three and fourpence; we're going to a dance." (Three and fourpence - 3/4 - for younger AnswerBankers meant 'three shillings and four pence' in the old, pre-decimal money.)
The game is also sometimes called 'Russian Scandal' or 'Russian Rumours' for obvious reasons...ie the story becomes embellished as it gets around. The title 'Russian Scandal' appears to be much older than the 'Chinese Whispers' version. The former is first recorded in the 1870s, whilst the latter appeared nowhere in print before the 1960s. I have no idea why people suddenly decided the game needed a new name.
Why Russian and why Chinese? Perhaps because such peoples were seen as particularly inscrutable or difficult to understand.