Maybe the 8th. This article doesn't even mention one which is suspected to have happened, the extinction of megafauna when humans came on the scene. If we're talking about extinctions Earth might have experienced, that deserves to be mentioned.
Considering the time scales at which the other mass extinctions happened, I don't think it's reasonable to count that as separate from what's happening now. It might instead be better to rethink the whole thing as one somewhat prolonged extinction event due to the appearance and subsequent activities of humans.
Sure. However, I don't see how the exact number of previous mass extinctions is particularly relevant to the idea that we're probably experiencing one right now, and we (humans) are the primary cause.
They are working from a particular definition of mass extinction which rules this event out. The megafauna that went extinct were a small percentage of the species in existence at the time.
