I have caught the reason of this problem. This problem exists in any browser if adobe flash player is not installed.
As for Chrome (which i use primary) Flash player is installed there by default. But if you go to chrome://plugins/
and disable flash player
you will get the same bug.
If have not found this limitation in known limitations "The current version of RadMediaPlayer works only in modern browsers which support HTML5. The functionality to play YouTube videos works in all major browsers, including modern and non-modern ones."
So you hope this can be fixed in telerik.