I just had a thought about the castle issue. The general claim is that castles fell out of use because cannons made them obsolete, and Europeans instead switched to a mix of dedicated forts and nonmilitary palaces. However, the segregation of palaces and forts was hardly a new thing in the world at large. The ancient Romans had palaces and dedicated forts, but didn't build true castles for the most part. Ditto for the Chinese dynasties. When you look outside of Medieval Europe, there is a wide mix of civilizations that either built castles or built separate palaces and forts, and cannons cannot be used as a reason for why these various civilizations made the choice one way or another.
I would actually suggest that cannons had nothing to do with why Europe switched from building castles to building palaces and fortresses. If you look at the broader picture, castles tend to be built in periods and places where power is heavily decentralized or where conflict is common. On the other hand, well-organized societies where power is centralized seem to tend to build a mix of civilian palaces and military fortresses.
Europe just happened to arm its armies with guns and cannons around the same time that it was making the transition from a decentralized feudal society to organized nation-states with absolute monarchs.
There's several issues regarding the progression of castles to fortifications. The classic castle definition I have been able to find is basically a fortification used as a residence for a local lord. By this definition, it would rule out the Edwardian Welsh castles that I think most people are happy calling castles so perhaps that really isn't a great definition.
On the other hand, calling any masonry (or even non-masonry) fortifications castles dilutes the definition of castle beyond what I'm pretty sure most gamers have in mind. It does for me.
But I think it is indisputable that effective cannons caused fortifications to change in character. I've posted enough basic links there and it doesn't take much study of military architecture to see that.
Combining the "lordly residence issues" with the "cannons caused forts to change" issue and you find by the 1400s you have two trends in Europe driving you away from high middle ages castles as states grew stronger and eliminated a placed for fortified lordly residences and cannons changed the nature of fortifications.
To the original post of gunpowder in a game setting, most settings I see and most artwork I see has fortifications like high middle ages castles. Many players aspire to build such a castle as well. Add gunpowder and it would seem that such style fortifications would change in a reasonably short period of time, forts would have to change their nature. It would not follow that cannons would necessarily change lordly fortified residences though. The former is technological and the latter is societal. Societies have their own dynamic and a new weapon system doesn't necessarily change the society (although it can). But ignore something demonstrable like the ability for a cannon to knock down high, thin walls and your castles will be rendered useless and you will lose any military advantage from their construction.
As to appearances and styles, yes there is certainly a subjective element to it. But I ask you, if you are "going to Europe to see castles", how many woud go to see star forts or roman forts? Some may add that to the itinerary (I would) but I wouldn't consider them castles.
I'll also ask you this, if a referee has a game setting that includes cannons and he also has a high middle ages style castle and you the PC want to get into the castle, wouldn't you be kind of annoyed if your cannon couldn't break down the curtain wall and even the keep in short order? They are good at that; the evidence for their efficacy is clear cut. If he does let you do so, it then begs the question why was such a vulnerable fortification there? They aren't exactly cheap.
Gunpowder changed fortifications. If you still want to call the result castles, in the end, I suppose that's an aesthetic issue. My aeshetic sense prefers fortifications that look more like high middle ages fortifications and I don't think that is especially unusual for the gaming population.
If I am going to modify foritifications for the gaming world, I'd rather do so for magic and monsters, not for gunpowder. I don't see what gunpowder weapons really add to the setting, personally.