After reading a little bit more on this issue, I think I can write a full answer.
Stephen Law's Evil God Hypothesis is about that if you can have an omnibenevolent god and the problem of evil, then you can also have an evil god with a problem of good. Furthermore, you can use all the classic explanations for the problem of evil that occurs when assuming a benevolent god, to explain the problem of good when assuming an evil god. It is not about proving or disproving the existence of God; it's about once you assume the existence of god, then why assume he is omnibenevolent?
Stephen Law says that many people say the universe shows signs of design, for a number of reasons which I will not expand upon here, since that's a whole other topic. However, if you assume that god exists based on this argument, then how can you assume that he is omnibenevolent? Evidence of design is no evidence of moral goodness, Law argues.
If you do assume an omnibenevolent god, then you have to deal with the problem of evil. It is clear there is a lot of suffering in the world, which many find a compelling argument against the existence of god. Bertrand Russell famously said: "No one can sit at the bedside of a dying child and still believe in God."
There are a number of ways to address this problem. One is the free will solution. In a nutshell, God gave us free will, and therefore, we can do good things and bad things. He had to do so to create creatures who are free. This is known as Alvin Plantinga's free will defence. The main point of criticism is that it only deals with moral evil (people choosing to do bad things), not natural evil (for instance, earthquakes or children dying from horrible diseases).
Another is character building. People need to go through some negative experiences to grow as a person and for that, some evil is required.
Yet another one is that you simply can't have good without evil. You cannot be charitable if there are no people in need, for instance.
And some people say that "God acts in mysterious ways". It would simply be arrogant to suppose that we can comprehend God's mind. What seems to be evil to us, is actually good for us, but we're simply not intelligent enough to see this.
Stephen Law uses these arguments (in a slightly different way) to explain the problem of good if we assume an all-evil god. Some examples below:
Free will
BOOBLEFRIP: God gave us free will.
GIZIMOTH: Free will?
BOOBLEFRIP: Yes. God could have made us mere automata that always did the wrong thing – the evil thing. But he didn’t do that. He gave us the freedom to choose how we act.
GIZIMOTH: Why?
BOOBLEFRIP: Because, by giving us free will God actually increased the amount of suffering there is in the world. He made the world far more terrible than it would otherwise have been!
GIZIMOTH: How?
BOOBLEFRIP: Think about it. God could have just tortured us with a red hot poker for all eternity. But that would have got rather dull for him rather quickly. How much more satisfying to mess with our minds – to inflict more sophisticated psychological forms of suffering.
Natural beauty
GIZIMOTH: Well, what about the glories of nature: sublime sunsets, stunning landscapes, the splendor of the heavens? We’re not responsible for these things, are we?
BOOBLEFRIP: No. God is.
GIZIMOTH: But why would an all-evil God create something that gives us pleasure? Also, why does he give us beautiful children to love? And why does he choose to give some people extraordinary good fortune – health, wealth and happiness in abundance? Surely the existence of these things provides us with overwhelming evidence that, even if the universe has a creator, he’s not all bad?
The “character-destroying” solution
BOOBLEFRIP: You’re mistaken, Gizimoth. Such things are exactly what we should expect if God is supremely evil.
GIZIMOTH: But why?
BOOBLEFRIP: Some natural beauty is certainly to be expected. If everything was uniformly ugly, we wouldn’t be tormented by the ugliness half as much as if it were laced with some beauty. To truly appreciate the ghastliness of the environment most of us inhabit – a urine stained, concrete and asphalt wasteland peppered with advertising hoardings, drug addicts and dog dirt – we need to be reminded every now and then that things could have been different. God put some natural beauty into the world to make our appreciation of the ugliness and dreariness of day-to-day life all the more acute.
source
So, what this effectively shows is that, if you derive moral goodness from the argument of design (or any other argument from which you shouldn't/can't derive moral goodness), then you can also derive moral evil from that same argument, i.e. you cannot draw any conclusions about whether god is omnibenevolent or not based on this argument alone. Therefore, deriving whether god is (supremely) good or not requires other arguments.