Considering how slow the stars move in the night sky there would really have been no change. In fact there would have been hardly any noticeable, to the naked eye, change since the first human being to walk the Earth looked at the night sky.
The comment referred to Tolkien's locale, not some astronomical aberration. Remember, the folks who did the sky are in America, not England. Also, the placement of the constellations in-game is based on comments in the books and extent sources, so there may even be a little variation between what's in-game and the actual sky.