> that structure is as/more important than sequence?

Structure is determined by sequence, so they are equally important. Structure is more conserved than sequence, mainly due to the physicochemical constraints that govern protein folding.

> that "reaction centers" are what matter, and the rest is just "protection"?

Sometimes not even protection. Many enzymes can have plenty of its sequence/structure removed and still be functional. Natural proteins carry lots of evolutionary cruft.

> What do you mean by "reaction center" - surely not physically central within the folded structure

I think they borrowed the term from photosystems/photosynthesis. But, to be more precise, what they actually meant is the active site of an enzyme; the location where the catalyzed reaction takes place.

> (isn't it the surface shape that determines reactivity) ?

Shape is not enough, the chemical nature of the amino acid residues involved is also important. A single mutation in a key catalytic residue will shut down the enzyme even if the shape stays the same.