Salaam to all,
A simple concept but varying opinions. Many things are a direct result of the progress of human civilisation where definitions change over the generations. Here's my take :-
As the prophets were sent to remind people of Allah, these messages were forgotten over time and Allah faded from memory. But they were aware that there is a supreme Being, however, they only lost sight of Who He Is. As a result made up a 'replacement'. All these replacements are false deities but needed a 'generic' name to classify them for human understanding, hence the term 'god', which loosely translates as the divine and binds them to their beliefs which were of shoots from the religious messages given by the prophets.
So over thousands of years and countless religions, all had a supreme being at the top. All of them were given specific names but who were they? They were the 'gods' of that particular faith/belief or whatever. We, in Islam know that they are NOT, but that is only us, in Islam, but what about the rest of the world? They had their beliefs too, and they believe that the 'Being' is their god.
So now there is a division on the term 'god'. Not so much for muslims as it is quite clear from the shahada that there is not other god but Allah... but not the whole world is a muslim and they still have their 'being' at the top of their faith.
So every faith has their 'god' or 'God' and for muslims, it is Allah, the One! As what has been said above, I agree 100% that Allah Is His Name. To know him we have to study his 99 names (asma ul husna) and when we refer to Him, we should call Him by His name - Allah (or any other of His 99 names). Like us, humans, we do not expect people to call us 'Hey, human!' but by our names. That is who we are.
Of course there is also a question of human etiquette where we do not want to cause offense by denying others of their god by constantly calling Allah as God. Hence, personally I would accept that god is used to to denote the 'being' at the top of the other respective faiths but Allah as the owner of the 99 beautiful names and Is THE Supreme Being of Islam.
Qul Yaa Ayyuhal Kafiruun as translated by Yusuf Ali
Say : O ye that reject Faith! [1] I worship not that which ye worship, [2] Nor will ye worship that which I worship. [3] And I will not worship that which ye have been wont to worship, [4] Nor will ye worship that which I worship. [5] To you be your Way, and to me mine. [6]
Peace