There is no dispute that the killing of Reeva Steenkamp was unlawful as it would be impossible to argue that Pistorius acted in self-defence (or private defence, as it is known in law). You can only rely on self-defence to exclude unlawfulness if an attack on your life (or the life of another), on your property or other similar interest has commenced or is imminent. This is an objective test, so where no attack actually occurred, one cannot rely on self-defence to justify the killing of another person, which you thought was necessary to defend yourself. No such attack occurred or was imminent in this case. (Whether the common law should be developed in line with the values in the Constitution to restrict the right to kill others in defence of your property, is an interesting question, which I cannot discuss here.)
The question then is whether the accused had the requisite intention to kill another person. Intention must not be confused with motive. The person’s motive is the reason why he acted in the manner he did and is usually thought of as irrelevant for determining guilt. Motive can explain why an accused formed the intention to kill another person, but is separate from that intention.
The state can prove the direct intention by proving that the accused actually meant to kill the deceased. Evidence that the accused and the victim were involved in a stormy argument before the killing or that the accused had previously threatened the life of the victim could be important.
It's this thing that "premeditated murder" exists in our law that gets me. There is murder and the premeditated part of the murder determines whether this is dolus directus, indirectus or eventualis. As the prof points out, this act at its very core is murder - it's now the defence of self-defence that will keep Oscar out of jail.