Despite the clear thinking that Stephen Hawking has done in the past on the place of humans in the universe, I think his point here is problematic. Drezner raises a number of concerns with Hawking's point as well - many of which revolve around strategic considerations. But I think he even misses another important point.
We shouldn't discount the prospect that alien life will have evolved cooperative, friendly, rational, altruistic tendencies and a robust sense of universal rights - perhaps even property rights. And just as a considerably more advanced alien society can be expected to have stronger biological and technological faculties than humans, we should expect them to have more advanced social faculties. Daniel Dennett highlights the fact that while life evolving on other planets will of course be considerably different from life on Earth, there are many "good tricks" that evolution will "discover" again and again. He gives the example of eyesight (for organisms evolving in a transparent atmosphere) as a feature that is so advantageous it is almost certain to evolve elsewhere. Other things, like a base-ten number system - are considerably less likely to evolve again and again because in all likelihood it emerged solely as a function of our ten fingers.
I would guess that cooperation, trust, and the recognition of some collection of universal rights are memes that would almost certainly evolve in an advanced species. Daniel Dennett reviews Dawkins's theory of memes here, and specifically points out the role that memes can play in overriding the underlying impulse to thrive and reproduce* (which itself is probably an evolved meme, or at least an evolved cocktail of hormones). Dennett focuses on destructive memes - like Wahhibism - but he also mentions more constructive memes, like the idea of memes itself! One of the most obvious "successful memes" is the ability to trust others, to cooperate, to exchange, and to recognize these things called "rights" which have no substantive or tangible basis but are nevertheless extremely important in human society. A great deal of research has suggested that it was precisely this ability of humans to trust each other and engage in mutually beneficial exchange (which is impossible without an understanding of property rights) that allowed them to dominate the Neanderthals (who did not have trade networks). Of course, this highlights the fact that cooperation and violent competition are not necessarily mutually exclusive. Yet in the last hundred years humans have worked to make the two mutually exclusive.
Why wouldn't we expect aliens to evolve that ability to trust, cooperate, exchange, and recognize rights? It seems like one of those "good tricks" that evolution will discover again and again. Certainly any civilization advanced enough to reach and destroy the Earth probably depended on some version of property rights and exchange to get to its advanced state.
Obviously, none of this is certain. We don't have a lot of evidence to draw from. Some form of trust and exchange seems quite essential to successful evolution: trust and exchange to the exclusion of violence and domination seems much less important and far more tenuous, based on the experience of our own society. But I think there's reason to be optimistic. As Adam Smith said, "the division of labor is limited by the extent of the market". Because trade, exchange, and cooperation are networked-based activities, they become more beneficial as the network grows. This is why I think there is an underlying tendency towards a global economy and a global government: and this tendency is implicit in the nature of trust, exchange, and cooperation. If it is implicit, then a unified planet operating on the basis of trust, cooperation, and exchange shouldn't be all that inconceivable. None of this is to say that a Spartan meme wouldn't also be evolutionarily fit. We seem to have demonstrated by experience that a Spartan meme completely devoid of out-group cooperation and trust is not evolutionarily fit - but who knows? I think Hawking is jumping the gun to just assume that aliens would be dangerous. They could be dangerous, but there's also good reason to believe that if they're more advanced than us, we may very well be the trigger-happy, belligerent ones.
*Dennett's characterization of the impulse to thrive and reproduce is somewhat problematic and at odds with another Dawkins idea - the idea of the "selfish gene". Ultimately, it is selection at the genetic level that drives evolution, not at the level of the organism. Many organisms themselves have evolved the tendency not to reproduce because it facilitates the reproduction of their genetic code through other close relatives. Dennett glosses over his point here, but I don't think it changes the argument substantively.