I don't know if they relish killing people any more than Rumsfeld does. It's very hard to figure out anyone's psychology at a distance.
But I think JH is right that alQ is a group of folks who aren't "organically" linked to the Moslem masses. It's not like Intifada-type "terrorism" which is more "spontaneous" (at least in the early stages) in the sense that it wasn't organized by anyone and is based in the righteous anger of everyday people.
One problem is that the word "terrorism" is applied to two or more distinct phenomena (which often show up in mixed form in the real world). Mass "terrorism" (like the early Intifada) might best be seen as resistance. It's a clear response to domination, oppression, and can be triggered by a specific insult (e.g., Sharon's visit). This is the kind of terrorism that is most likely to be encouraged by poverty.
On the other hand, there is elite terrorism (e.g., the Red Army Faction or the Bush White House). (The latter example likely has more organic connection, since it gets a lot of at least passive support from US yahoos, Israel apologists, and the like.) This is where the poverty/terrorism connection is extremely weak if not non-existent. However, individual members of the "masses" may join elite terrorist groups because of poverty. Also unemployed members of the middle classes are more likely to do so. Such events as the US/UK war against Iraq could also be a contributing factor, a trigger. JD