Blasphemy is perhaps the most reprehensible thing there is. It is so unthinkable that this mitzvah is called “birkas Hashem,” blessing God, when, of course, we really mean the opposite (God forbid). Like Jews, non-Jews are not permitted to curse God. We see this throughout the Book of Job. When Job’s life goes completely down the tubes, he is advised to “curse God and die.” This does not mean that doing so would cause Job to be Divinely struck dead; it means that he would be liable of the capital crime of blasphemy–and Job was a non-Jew.
This mitzvah includes not only a prohibition against blasphemy but also against desecrating God’s Name. The obligation of non-Jews to pray also falls under the aegis of this category.