No matter how many times you look at it, the novel and the 3rd game along with its manga cannot exist together.
In my opinion, the novel is a "what if.." situation. Something alternative that could/may have happened but did not.
First of all Dante absolutely thought that Vergil was dead. In fact even in Devil May Cry (I mean the first game) Dante believes that Vergil died along with his mother when he was little. He said so when Griffon died. Dante: "Mundus..his heinous way make me sick. Killing one of his own..like they were nothing. He's the one who took the life of my mother..my brother..for sure......"
Here's the cut-scene too
Griffon Dies.
When they changed the whole thing in Devil May Cry 3: Dante's Awakening and the Manga was out, they re-modeled the whole thing. But in the Manga he clearly thought Vergil was dead before their meeting. Why? Here's why.
Proof 01.
This clearly shows that when Dante survived the attack that killed Eva, he thought that he lost both of them. If Dante had took a hint that Vergil escaped that place with Yamato, he would run after him or search for him. They were close brothers before that after all.
Proof 02.
In here we see that Madhater says that Dante in order to tempt him to join them along with Vergil. If as you said, Madhater was a freaking idiot who made false assumptions then Dante wouldn't be the least surprised. After all he wasn't surprised when he heard he had an invitation from Vergil after they had a year to meet, in Devil May Cry 3: Dante's Awakening. Because he knew he was alive, and did not care if he was around or not. If in the manga knew that he was alive, he wouldn't care if Vergil was in the town or not.
Proof 3.
As you can see in here Dante clearly says to Vergil that he thought he was dead. If that's was Dante's idea of being funny instead of the truth then he would say it in the game as well. As he's the guy who likes to say his jokes more than once. For example he always speaks about the bathroom when someone enters his shop
Therefore, he absolutely thought Vergil was dead before that.
Proof 4.
In the novel, Dante receives his twin Handguns from a female gunsmith. However, in every game their description states that he personally made them. Ebony & Ivory "Dante's personal hand-made customized twin Handguns".
Proof 5.
Gilver used a shotgun to change Dante's attention in the novel. If that was the Vergil we all knew and love, he would have used a Summoned Sword instead. You may say here that he probably wanted to conceal his identity by not using such a "Signature Attack". That cannot be so, since if he had succeeded (which he clearly thought he would) then Dante would have been dead anyway.
Proof 6.
After the novel Dante opens Devil May Cry (the shop). While in Devil May Cry 3: Dante's Awakening, it clearly showed us everything about the shop. How he decided what to do with it, its name, etc.
Proof 7.
Dante's character in the novel. He is dark, stylish, serious and tough. Awesome character, and very close to the image Dante showed in the first Devil May Cry. However in Devil May Cry 3: Dante's Awakening he's just a cocky teenager with attitude (in the beginning). Weird no?
The fact that Capcom worked closely with Anime/Manga/Novels doesn't say Absolutely Nothing to me. The guys contradict themselves infinitely in the Devil May Cry universe.