I don't think there's anything particularly necessary about gunpowder for industrialization, but I'm not sure what industrialization would look like without explosives for mining. Industrialization requires lots of iron and steel, and I don't think iron ore can be mined effectively without explosives. So I think we'll see one of two things:
1) Another non-gunpower explosive is developed for mining purposes. Eventually, people realize it can be used for weapons, and firearms are developed. I think in the end this would look very much like OTL but maybe with a little bit cruder weapons.
2) Some other mining technique is developed that doesn't require explosives. I'm guessing lots of ridiculously cheap slave labour fuels the mining necessary for industrialization. Maybe eventually, the slaves are replaced by giant rock-drilling machines. I can't see as extensive industrialization as OTL this way as, as far as I know drilling is a lot less efficient than explosives for mining. This might be an interesting world to explore, although I'm not sure how you'd be able to prevent the discovery of explosives....