It would be a enormous breakthrough if this works as they say. One possibility is to use a modified lenivirus (such as HIV itself) to insert the gene for this enzyme. The promoter for this gene may even be able to be designed in such a way that HIV infection triggers the gene to become active, which would in turn excise the HIV from the genome. Also tied to the promoter could be a gene for a transmembrane protein or internal signaling molecule to trigger the cell to be destroyed and prevent the already produced HIV from being released.
A safer alternative to the lenitvirus approach would be to use a nanoparticle encapsulating the DNA for the gene and the required enzymes to integrate it into the genome (or even leave it as a plasmid. I'm not sure though if human cells will express plasmid vectors, though I know some eukaryotic cells do). This approach has been successful selectively targeting and delivering drugs (one paper used alpha particles) into cancer cells.
A safer alternative to the lenitvirus approach would be to use a nanoparticle encapsulating the DNA for the gene and the required enzymes to integrate it into the genome (or even leave it as a plasmid. I'm not sure though if human cells will express plasmid vectors, though I know some eukaryotic cells do). This approach has been successful selectively targeting and delivering drugs (one paper used alpha particles) into cancer cells.