Summary: they found a document with checksums for each of the 36 banks of the missing software. This let them know that two banks had changed. Working from an earlier and later source listing versions, they had to recreate only some of the changes. Luckily, they found memos describing the changes - mostly in a newer gravity model. All that was left was to put the code in the proper places, and some obvious guesses (e.g. new constants at the end of existing constants) -- and it worked!
We aren't printing out our source code any more. Which means that such recovery methods won't work in the future. Has archival of such historic stuff improved since?
Granted, this is only a snapshot, and preservation is a big problem. And you can't easily preserve gigabytes of data in dead tree format...
Generally the best approach is "Lots of Copies Keep Stuff Safe" but moves to streaming media and game rental services worry me.
There also needs to be a recognition that what we see is often a very small fraction of what existed... most things won't survive, unless successive generations of people continuously care sufficiently about them. Or they're ubiquitous that we'll find at least one...
My older media is all pretty much unreadable for one reason or another. My solution is to buy new drives every year and copy everything forward. Fortunately, the capacity keeps rising so that works out rather well.
In many cases it will prove difficult to even be able to build or run software that hasn't been touched in 10+ years. Preserving the computational environment is a whole another concern for future software archeology.
A fun watch.