Knuth thinks in algorithms, not solutions. In his day, people were constantly inventing new algorithms--if you've never done it before, you should at least be able to guess that it's a big rush. That's what Knuth thinks of programming as: a series of completely new inventions and associated rushes.
What he's actually trying to say was that, as a usefully large number of algorithms for everyday tasks have already been discovered (optimally, even!) and codified into "libraries", people are running out of (easy) things to invent, and so aren't getting that rush as often. What was needed, in his mind, was a replacement for the rush, as that was what he saw as the raison d'etre of programming; being a mathematician himself, it was probably the only reason he programmed at all!
Of course, we've gotten on just fine without the rush. "Programming" as solving problems has continued to flourish; Knuth's "programming"--really referring to the scientific method applied, as it should be, to Computer Science--has quieted. It used to be that every programmer was a practicing computer scientist by necessity, just as every astronaut is currently an astrophysicist by necessity. When "platforms of discovery" (computers being one, the vacuum of space being another) mature, the need (or ability) for their practitioners to be involved in the creation of the theory underlying the field diminishes. This doesn't mean the field "dies"--it merely segregates.