It is the responsibility of the person making an extraordinary claim to provide proof of that claim. Since it is impossible to prove a negative (except, perhaps, mathematically) there would be little chance of my proving that they are not divine in origin.
However, it is possible to show that the likelihood of that is so far removed from reality as to be next to impossible.
The article states that these "religious and moral imperatives" were "authored by God" "according to the Hebrew Bible." And what proof does the Bible give for this? Only that it is the written word of God. And how can we be sure it is the written word of God? Because the Bible tells us it is! A bit of circular logic here, isn't it? While the Bible is certainly a historical document, it is not a history book! There is no evidence outside the Bible that Moses existed or that the Exodus even took place.
Even if we assume that there was an actual Moses, how do we know that the Commandments were given to him by God? We only have his word for this, after all. He went up the mountain alone, and no one saw God hand him the tablets.
Perhaps the fact that there were at least eight previous codes can give some insight into the true origins of the Commandments.
And just as an aside, which version of the Commandments are we supposed to follow? Those given in Exodus 20, those in Exodus 34, or those in Deuteronomy 5?
While it's true that none of these items constitute proof that the Ten Commandments were not divine gifts from God, they do cast significant doubt on that hypothesis. And with the only evidence for that assertion being the words of some 11th or 12th century BC nomads I think we have to lean more towards doubting the Bible than accepting it.
After all, in the words of Dara O Briain, "It's only the Bible. It's not gospel."