This is technically correct. But from the perspective of a non-technical audience, calling it an "ad cookie" makes a lot of sense. It conveys a lot more information about why people should care, and why Google and others might be reticent to end their usage.

Maybe an "ad-enablement cookie" or a "tracking-enablement cookie" would be better. But the technical term of art, "third party cookie," is french to most people. As long as they make a note of the technical term (it's in the first line!) I think they're well within the limits of journalistic license.