While it may be possible in theory to patch/fix the cancer cells, you'd need a virus that can target them specifically. In the case of using HIV here, it's because it's so efficient at getting into the immune system that it can be used as a vector to reprogram it. I've got to imagine that other "super viruses" could be used in a similar manner if they also target things so well.

simcop2387 is right in that the biology here gives them a leg-up on what would otherwise be an even more difficult problem. The whole class of lentiviruses (of which HIV is part) are useful for delivering genes to target cells. In this case, HIV is very good at finding T-cells which are exactly what whas needed here to trigger the immune response.

You are correct that they are using the HIV virus to reprogram the T-cells. They basically are making them express a very specific protein on their surface which allows them to seek out the tumor cells. When they find one, that protein is "wired up" to the cells' ordinary immune system genes that do their thing as they normally would.

Basically, the T-cell is like a hit man. It shows up, punches a bunch of holes in the target cell's membrane. Then it dumps a bunch of enzymes in there that go in and break important stuff. Once the chaos reaches a certain point, the target cell decides all is lost and it pushes the big, red "self destruct" button and goes through programmed cell death (apoptosis).

The actual work to make the viral vector and test it in mice was published in a study in 2009, so this new article is news because it's the follow-up where things were done in humans the first time (and they actually worked). From looking over the literature, apparently people have been trying this for some time but it has been failing for one reason or another.