Edit: They must have contingency plans for such scenarios. That's part of the job. But I think that it is not possible to keep to the initial schedule, so I'm guessing that the plan is to re-despatch ASAP to minimise delays while displaying the standard "delayed-apologises" to customers.
Remember also that the total loss of the plane impacts more that this single flight. Like airlines, I am sure it had an utilisation schedule, and now it's gone so they'll have to account for that.
That's why they do have contingency plans... And that's why they develop them with a cool head. Because when disaster strikes people tend to get emotional.
Edit: Wikipedia says that Amazon Air operates 39 planes. Sudden loss of one has to have an impact that has to be planned.
Anyone who operates a whole fleet of 767 has a plan in case of a crash. That's the most elementary professionalism.
That's certainly smaller than Delta's ~800 planes, but they're certainly not tiny.
Grounded for unknown timespan due to some kind of severe damage = does happen from time to time (good thing, because otherwise, crashes would become more likely...)
Since the effect on the logistics chain is identical (at least apart from that single shipment in question), you just use the contingency plan for the latter when the former happens. And for the latter, you MUST have a plan.
As far as I know, zero customers complained about the obviously tragic and unusual circumstances of the delay.
For Amazon, they almost surely know with immediate certainty what was on the plane, and are mostly selling from stock, making the resolution easier in some ways (though larger scale on the other hand).
We treated this response as an ad-hoc process and have zero plans to systemize the response to a once every few decades issue.
That said, Amazon is a logistical beast and regularly deals with transport failures (semi-crashes, lost containers, train derailments, fires, etc) so I don't feel that this would necessarily warrant any out of normal response.