As I read it, they mean the change at 50% (actually the change is at their “announced discount” which we presume to be 50%, but could conceivably be 55% or even 60%) regardless of channel. So, yes, sales at 50% are a $2 royalty per copy, and sales at 51% are $0.98, as long as those sales are either made on a non-returnable basis or are considered “special sales”

In my experience this is the case in contracts with most large trade publishers. I’ve also seen contracts from Henry Holt & Co. (part of the group that owns St. Martins Press), Bantam Doubleday Dell (now part of Random House), and children’s book publisher North South Books. All these companies had similar clauses in this respect.

The idea here is there comes a point at which the discount is so high that the publisher isn’t making much money at all on the sale. Because the publisher isn’t likely to make these sales (and doesn’t unless the quantities are large enough) and because they are nearly unprofitable, the publisher wants the author to “share the lower margins.”

It is an abrupt drop, and some contracts drop the rate more gradually (for example, 1/2% for every additional 1% of discount).

In practice it isn’t very worrysome because Publishers don’t normally sell books at these discounts. The average author will never see such sales on the statement. More likely, the author will see a ‘remainder’ sale on which he gets no royalties.