I just watched Olivier's Richard III. I was impressed by the layers of the play.
At one level, the play is driven by the propaganda of the day that the House of Plantagenet destroyed itself, and that Queen Elizabeth's grandfather, Henry VII, the first of the Tudor kings had saved the nation.
I suppose at another level the play, which is actually the fourth in a set of history plays, is the culmination of the tragedy of the House of York, as the misdeeds of the members of the House lead to the most evil member of that family who kills the last remaining members before his misdeeds lead to a revolt which ends his own life.
In the play as Shakespeare wrote it (but not as Olivier and the movies rewrote it) there is apparently a Cassandra like character who curses each of the doomed characters, explaining what that character has done to merit the curse and destruction, and the curses of course come true. This would add another layer to the play of preordination, in the sense that evil deeds lead to one's destruction as well as that the curses are working themselves out.
Shakespeare must be considered, as a man of his time, to believe in the divine right of kings, so that Edward IV, Richard III and Henry II must have had that right. In some sense the story must be seen as one of fate unfolding as was preordained.
Yet the play at another level is that of Richard, Duke of Gloucester manipulating his way to the throne and then, by his evil nature, continuing in manipulations that drive away his supporters, disgust the public (and the audience), lead to rebellion, and eventually to his defeat and death. Shakespeare succeeds in making this a tragedy in the sense that the audience is brought to identify with Richard, approving as he brings down those whose evil deeds were exposed in previous plays and rises to the throne, only to be undone by the flaws in his own character. It is the murder of the princes, sons of Edward IV, in the Tower of London that marks the second part of the play, since they did not themselves commit sins meriting their deaths.
I suppose the play can also be seen as a lesson in Machiavellian statecraft, in which the prince does what is necessary to secure the throne, but then fails to assume the beneficence of the successful ruler and thus loses his throne and his life.
Finally, of course, the work is hugely successful as a work of theater, its language, structure and characters grabbing and interesting audiences for four centuries.
I suppose that one sees today the similarity with Gaddafi and other would be kings who are getting their comeuppance today, or Hitler and Mussolini in my youth. I suppose Shakespeare's English contemporaries saw parallels in their own time.
That surely must be one aspect of Shakespeare's genius, creating works that could be read at so many different levels, relevant to so many different times and places.