There is no magic. I don't know what Directed Edge are doing, but simpler Amazon-style recommendations (people who bought X also bought...) doesn't need to precompute anything if you choose your data structures properly: get a list of things people bought along with X, count them (or actually store them counted), optionally normalize for general popularity, sort in decreasing order, show top results.
Amazon's algorithms are simpler than our own (at least as far as I can tell) and most recommendation engines use some sort of embedding to reduce the dimensionality of the problem.
Amazon's related products do in fact seem to be, or very near to, a simple counting structure. Our ranking algorithm builds a large subgraph around an item and then does a few passes with a couple different ranking schemes to try to figure out the hot items within that subgraph, prunes "noisy" connections (i.e. links that are "hot", but don't actually pack much semantic meaning) and then tries to scale things so that the results returned aren't simply those with the largest overlap, but those that are most relevant within that subgraph relative to the larger graph. In that sense, it has some similarities to web-search algorithms.
In user-visible terms, that means that our results are often less obvious than Amazon's recommendations -- for a long time we called that the "tell me something I don't know" problem. It's no good to do a search for "Miles Davis" and have "Jazz" com back as a related item. If you know about Miles Davis, you already know about Jazz.
If you mean metrics, the only one that I find really meaningful is a feedback loop to see what users are in fact interacting with, and we'll have something in place for that shortly. Synthetic metrics on recommendations quality don't really impress me because they ignore that recommendation algorithms are solving an human-computer interaction problem as much as they're solving a k-nearest-neighbors problem. I've got another article in the pipe on some of the interesting problems of ranking on real data, but it keeps getting pushed back since there's you know, a lot to do at the moment. :-)
I'd love to hear something from wheels though.