They have to care in some circumstances unfortunately, if they are aware of an IP infringement and don't action it, it can be used as evidence further down the line for bigger infringement cases.
Trademark is the only form of intellectual property (IP) for which selective enforcement is a problem. Presumably the name of the game is trademarked but the images & audio are covered by copyright law, not trademark.
IANAL but if Blizzard is aware of this copyright infringement and do not act on it, the developer can go for an acquiescence defence. If successful, Blizzard surrender their rights in that particular project.
This could potentially have an effect on the value of their IP which can give leverage to potential acquirers/investors.
No. There is no such defense in U.S. copyright cases. Again, only trademark requires them to pursue infringement to maintain their protection, and by extension, value.