What volumes of the graphic novel does the XIII adventure game cover?
A review of the game mentions this:
[T]he plot is basically a retread of what’s been included in the previous game[.]
The previous game covered the first 5 volumes, so if you've finished volume 5, you should be fine.
Note that the review also states that this is more of a "hidden object finding" game than a traditional adventure game. It might be worth reading the review before you pony up the cash to make sure you're interested in what you're buying.