The physics/economics definition is basically that time average = ensemble average. (The term "expectation value" is used in the Nature paper you reference, but that amounts to the same thing.) But individuals do not experience the ensemble average. A condition on averages is not the same as a condition on individual outcomes.
Which could be equal to the time average, and thereby satisfy the definition of "ergodic" that was given, without in any way contradicting this:
> while individuals are unable to realize their expected value because they only have one lifetime.
I am not disputing that this happens. I am only disputing the use of the term "non-ergodic" to describe it, or the term "ergodic" to describe a hypothetical world where every individual experienced exactly the average outcome.