Compared to most fantasy novels, Pratchett is totally rocking an informal style here. Most fantasies, especially in the subgenre of epic fantasy, are written like they're meant to be historical textbooks or performed at a Ren-faire. Instead, The Color of Magic reads more like you're meeting Pratchett for some drinks, and he has a really funny story to tell you.
Let's do a quick comparison. Here's an excerpt from George R.R. Martin's epic fantasy novel, A Game of Thrones:
They watched the heroes of a hundred songs ride forth, each more fabulous than the last. The seven knights of the Kingsguard took the field, all but Jamie Lannister in scaled armor the color of milk, their cloaks as white as fresh-fallen snow. Ser Jamie wore the white cloak as well, but beneath it he was shining gold from head to foot, with a lion's-head helm and a golden sword. (29.3)
And we're going to stop there because the description of all the tournament's participants goes on forever. Martin's fantasy is typical of epic fantasies and brims with these long passages detailing the armor worn by knights or the architecture of a given city. The sentence above is only the beginning of the description of Jamie's appearance, and it's one of the shorter ones to boot.
The novel is also filled with archaic word choices. No one ever "has breakfast," for instance—rather they "[break] their fast" (15.1). Don't get us started on how many times people ride out "on the morrow" (8.1). All. The. Time.
Now let's consider an example from The Color of Magic:
"Ahaha. Yes," said Rincewind. "Hrun, isn't it? Long time no see. What brings you here?"
Hrun pointed to the Luggage.
"That," he said. This much conversation seemed to exhaust Hrun. Then he added, in a tone that combined statement, claim, threat, and ultimatum: "Mine." (2.10.32-34)
The difference is pretty obvious, isn't it? Rincewind's greeting of "long time no see" is a very casual, very modern word choice compared to the fantasy setting. The sentences are also short and get right to the point. Sure, in other parts of the novel, Pratchett allows himself a more vivid description of a character or detailed passage about the setting, but even these have a no-nonsense approach, except, of course, when nonsense is exactly the point of the matter.