To my mind (as a cancer biologist), the big caution here is in the mouse xenograft model. While it is good that they tested some different cell lines (in a dish), it is much easier to cure a xenograft tumor than it is to cure a sporadic tumor in a human. This is probably because culturing a cell line in the lab for a while tends to reduce the genetic heterogeneity among the cells, and so reduces the chance that there will be a resistant mutant among those cells. Clinical experience shows that there is very often a resistant mutant in the sporadic tumor of a human patient (particularly if the cancer has managed to spread, i.e., metastasized). In any case, they only tested one cell line in the mice. So it is time to try more.
Second off, the cancer stem cell hypothesis is highly controversial, and has been mostly demolished in breast cancer (the type of cancer in this experiment), where Kornelia Polyak has shown that what people are calling cancer stem cells, are probably just different clones / cell types in the tumor. That being said, if we can come up with drug combinations that can handle all the different cell types in a tumor, we'll be doing a lot better than present.
It certainly is promising that the combined therapy showed no relapse over ~60 days after the end of therapy, but I'd like to see the results taking out further to see if the mice would relapse later. I'd also like to see it demonstrated on other cell lines and more realistic models of cancer. There is a long history of drugs looking good in simple "pre-clinical" models, like mouse xenograft models, and then failing in clinical trials.
Also note that it usually takes decades between initial discovery and changing clinical practice, so don't hold your breath, but do cross your fingers.