The Church launched a court case to challenge the directive, arguing that the word Allah had been used for centuries in Malay-language Bibles and other literature to refer to God outside of Islam. But authorities say that using Allah in non-Muslim literature could confuse Muslims and entice them to convert, which is a crime in Malaysia.
Two things. Not only has Allah been used to refer to God by non-Muslims but so has the common Muslim greeting. This isn't really about who may use the word. It is really about the possible "criminal" conversion of Muslims to other religions.
It's interesting, because one of the claims that is commonly given by those adherents to Islam is that it is a universal religion and there is only one God. Well if there is only one God then why would any Muslim with such an understanding be bothered by any non-Muslim referring to Allah? Because it's not really about recognizing the One God. Rather it is about recognizing a specific way of worshipping that One God.
This is really about control. This is why in such places where the most insecure Muslims congregate there are laws against conversion (formal or informal). There are laws against speaking ill of the religion (formal or informal). There are laws against speaking ill of the Prophet (formal or informal). And those laws apply, oddly, to those who do not ascribe to said religion. It would be one thing if such laws (outside of conversion) were only applied to Muslims. That's fair. If you are in the group you abide by the rules. But when others are subject to the rules of the in group, then you have a whole other issue.