I detest articles that use the word "cure" and "cancer" in the title. They are without fail so breathless about the clichéd achievement that they are exploiting in the headline that they either fail to acknowledge the real magnitude of the problem or gloss over it with practiced sleaze (not sure which happened to the writers here).
We've had a "cure" for cancer since the times when barbers also performed surgery on the side (Egyptian civilization, at least), and that is surgical excision. It's still the best treatment we have for many cancers, e.g. melanoma and lung cancer, both of which are much more common than the cancer in the article. It doesn't work for every cancer, but for some cancers it works good enough, and even better when combined with chemotherapy (which ham-handedly slows replication in every cell in your body). The point of any cure is to remove the cancer cells from your body and for some cancers they fortunately stay within one excisable area.
Like the GP comment pointed out, this is essentially a much more targeted version of the same thing. Obviously it would be better for the patient to retain B cells, without which they will have no adaptive immunity--just like a patient with melanoma would prefer to keep the hunk of their nose that the surgeon had to remove. This is an incremental, very fancy and very expensive improvement on the same old strategy of killing the organ to save the body. It will never work on non-blood cancers (which are the vast majority of cancers, BTW).
People do not understand that cancer is a disease that combines the trickiest parts of fighting aging with the trickiest parts of fighting infectious disease. Cell replication is one of the hardest things your body has to do, and it does it several trillions of times per day in your body, essentially copying about 1 billion TB worth of data while automatically detecting and fixing every dangerous error that could possibly result. It is natural that this process will screw up catastrophically at some point--on an infinite timescale, assuming we fix all other health issues, everybody will still get cancer just as surely as they age every year. And once they do, you have a cell that your immune system has carefully trained for decades not to engage, invading and hogging every resource it can, with mutations that allow it to adapt to selective pressures, including any drugs you might throw at it. Essentially, it's an infectious parasite, except it looks 99% like your own cells to your immune system, and is already perfectly suited to your body's style of metabolism.
Let's keep in mind that this can arise from any cell in your body that replicates, and just about every organ system has a good number of those to replenish malfunctioning or old cells and fix injuries. The possibilities are staggering and so are the number of known cancers.
There is no "magic bullet" that cures every single cancer, just like there is no "magic antibiotic" that kills every infectious bacterium. Even the smartest, most generalizable ideas right now, like cancer vaccines, depend on your immune system to make the final push, and the immune system is just as fallible as any other organ system. At the point where somebody can make the claim that all cancer is cured, we will as a matter of course have gained control over every replication event that occurs in our body (trillions upon trillions of nanoscale events per day). That will be a truly remarkable feat, but is in no way within reach of any foreseeable technology.
When we cure cancer, we will have by necessity cured aging and all infectious disease will have become a relatively trivial problem. That should put the claim of "curing cancer" into perspective.