Does anybody know what type of chart that is? (some sort of bubble chart but with links between bubbles)
I'd just call it a directed graph (digraph) where the nodes have values (fields, attributes) which are expressed as visual attributes (size, color, label). I'm using "graph" in the mathematical sense and not as a synonym for "chart".
Such graphs can be drawn with graphviz, and other software. (Though I'm not sure how to achieve the gaudy 3D effect.)
[Edited once for each comment so far: Greg Snow, whuber, and Henry.]