Those are two separate charts/measures - continuing claims and initial claims. Initial claims have very much recovered. Continuing claims (which you posted) are below the last 4 cycle peaks but still above the last cycle trough as UE is 7.5%
You're right, I posted continuing claims and the quote mentioned initial claims, but personally I don't see that much of an improvement. I mean, we're still worse off than we were during the financial crisis. It's also interesting to note that last week claims numbers (both initial and continuing) were revised downward.