M.David Cancel, CTO of Compete.com, was kind enough to leave a comment stating that "Attention measure is calculated using both "time" and "traffic" (measured by unique visitors), not simply based on time". Later in the same comment, M.Cancel says "Although unique visitors and page views are critical pieces of the puzzle - these metrics often fail to accurately measure engagement". Again, implying that "time" can be used as a valid measurement of "engagement" is, in my humble opinion, totally wrong.
Michael H. Goldhaber most recent post reinforce my opinion. M.Goldhaber is not just another blogger... he's been writing about the concept of Attention Economy since 1985 and is the author of a paper that became a classic in the field: "The Attention Economy and the Net", published "way back" in 1997.
Here's what he as to say about "time" and "attention":
It is commonly thought that attention can be equated with time. “I will give you fifteen minutes of my time,” often implies that speaker will pay attention for those fifteen minutes. It would be a mistake though, to think that this formulation means that attention is particularly tied with time. All human activities — eating or walking just as much as paying attention— occur in time, and each one has some duration. But the time taken has little to do with the quality or even the intensity of the attention paid.If you would like to better understand the concept of the Attention Economy, read the book "The Attention Economy" by Thomas H. Davenport or the more recent "Competing on Analytics".
Conclusion: time ≠ engagement ≠ attention
Is "time" a component of "engagement" and "attention"? It certainly is... but we need to find the right equation!