It's a good question, and vidarh's response that "it's right there in the article: chilling effect" is clearly not helpful, since your question still applies without modification.

Looking through the memorandum, it appears that there are different levels of need/importance the government must establish depending on whether they are requesting information that could chill free speech. That is, warrants are granted more liberally for information that does not have a tendency to suppress speech (e.g., the date you filed for your car registration) than info that does (e.g., the list of books you've checked out at the library). The latter category must be shown to be more directly related to the issue of the case, rather than being merely a search for possibly-useful background info.

Amazon is arguing that (1) Alexa searches are of this second, more protected form of private information, and (2) the government has not met the higher burden of showing their importance to the case.

That, at least, is my reading of the memorandum. I am not a lawyer.