Parody is a specific legal defense against trademark infringement. The idea that trademark holders are always required to 'defend' their trademark regardless of context is simply false.

Given that the use here is noncommercial (Peng! is not selling a product in Google's area of business), it's almost certainly the case that Google is under no obligation to engage in any legal action. Even commercial parody can be protected, though the criteria are somewhat more complex.

Interestingly, it's easier to legally parody stronger trademarks because of public recognition of the parody - see Louis Vuitton v Haute Diggity Dog for an example. Google certainly qualifies as a strong trademark, although the parody name here isn't as memorable as 'Chewy Vuiton'.