On the one hand, I can definitely see why they chose to make a book about Arthas; main villain of the current storyline in WoW, he was a large focus of Warcraft III as well. The whole "former prince betraying his kingdom" is actually something I haven't seen done as well as Arthas has.
The book was fun to read because the characters are well-fleshed out and done in a way that reveals new parts of them; Kate and I were both surprised by how much Kel'Thuzad steals the show; for an undead skeletal magus, he shows a lot of emotion. Throughout the book you see Arthas growing up, trying and learning new things, and I think the author does an excellent job tracing what made him turn into the man that he is. Throughout the book I had fun trying to differentiate between what was Arthas' own personality and desires, and what was the influence of the Lich King. Now the thing about the book is, unless you are already into WoW or interested in it, this book will not have a lot to keep your focus.
Arthas himself is well done as a character, but truthfully they don't do a lot with him. I suspect that Blizzard dictated rather tightly what line the story would follow, and the author suffers a bit for it; the book is short and I found myself wanting to read more. Someone who hadn't played Warcraft III would not be able to predict most of what happens in the book, but I think someone who hasn't would not be very interested in what happens to the characters.
I enjoyed reading the book but would not be able to recommend it to someone who wasn't interested in the Blizzard games that it follows. The author stuck very well to the story line she was writing about, but one of the things that made her other story, Lord of the Clans, such a delightful read was the little bits of flair and things outside of what's already known about Thrall that she added in there. In conclusion, if you're interested enough in the book to want to read it, I definitely suggest you do, you'll enjoy yourself. But if you aren't and don't play World of Warcraft, then you'd be all right skipping it.