I found the source of the problem. First the solution - you need to press F5 within in the game screen.
Now detailed explanation follows.
Because of optimization some information that webpage needs is stored in the external files such as CSS files (describes the webpage layout) and JavaScript files (describes the dynamic functionality of the webpage). By having this information in separate files allows the browser to cache it. In other words, the files are downloaded only the first time the user views the webpage and on the next visit the browser reuses the files stored from the first visit.
The upside is that it reduces download time of the webpage. The downside is however, that if these files were changed in the meantime the user will not have the updated files and will see the webpage with outdated ones. In this case he has to manually command the browser to throw away the cached files and request new ones. This is done by the F5 button.
Problem is that F5 may not work all the time, because of the specific browser configuration. In such situation you have to clear the browser cache manually.
How to do this?
Opera:
Tools -> Delete private data -> Detailed options -> select Delete entire cache only -> Delete
Firefox:
Tools -> Clear recent history -> select Cache only -> Clear now
Chrome:
Tools -> Clear browsing data -> select Empty the cache only -> Clear browsing data