It is technically k-means, seeing as there are always k=6 or a user specified number of colors reported regardless of the input picture. What k-means algorithm they are using though is uncertain. Could be some form of quantization, or a lloyd type k-means. Could also be hierarchical agglomerative or many-many others. What would be interesting to try out would be some non-parametric clustering algorithms like the image recognition staples mean-shift and dbscan.