I was thinking the same thing. If it was all localized to a Pi then yes, but outside services isn't really DIY so much. Maybe half DIY if such a thing.
This is another example of what the GP comment is complaining about. It's not a DIY Alexa. Alexa is the virtual assistant API. This is a DIY Amazon Echo that still relies on the Alexa service.
As an engineer and a technologist, I agree that you and GP are precisely correct.
If you showed it to and asked a string of randoms off the street, I think way more than half would agree with the "DIY Alexa" label as reasonably communicative description and more useful than a longer but more precise title.