"Why is this considered struck through and not a lamination error?"
Because what you see is the impression of an object that got between the die and the planchet as the coin was struck.
A lamination error would be caused by a poorly made planchet and a layer of metal would be peeling or lifted from the surface of the coin.
With a lamination error, you wouldn't expect to see such fine outlines to the affected area and you would expect the surface of the affected area to be a little rougher.
I hope this helps,
Bill