Yes, Amazon is claiming First Amendment protections for their users of Alexa and NOT for Alexa "herself".
But let's not have that interfere with the sensational title of the linked article: "Amazon argues that Alexa is protected by the First Amendment in a murder trial".
Contrary to that title the author wrote:
The heart of Amazon's claim is that Alexa devices could provide insights into a person's entire life, and having two days worth of audio would be an unreasonable invasion of that privacy. Knowing that law enforcement has the ability to request data from these devices and peruse them at will would have a chilling effect on people using the services--which clearly would be bad news for Amazon's business.
"Such government demands inevitably chill users from exercising their First Amendment rights to seek and receive information and expressive content in the privacy of their own home," Amazon lawyers wrote, "conduct which lies at the core of the Constitution."
[adding bold and underlining, clearing up smartquotes and another annoyances]
Well, in that case, maybe they shouldn't have made something that relies so heavily on snooping on their owners? I could only hope that abortions of privacy like Echo / Google Home are tainted by this investigation and subsequent realization by the public that they're adding to their own police dossier.