This is what your normal immune defenses already do. While some white blood cells (neutrophils, monocytes) fight bacteria by "eating" them, viruses are too small to be directly attacked this way. Instead, they cells they infect have to be destroyed before they can release their viral burden. That's what cytotoxic T cells do. They recognize antigens on infected cells, and kill them by triggering apoptosis (programmed cell death).

What is truly unfortunate is, this doesn't always work. Some viruses are able to "hide" in their host cells, preventing them from activating the immune response, and persist idefinitely in a latent state. This is why you can't really get rid of herpes, once you have it.

What looks promising about this development is that it seems to target a form of RNA that is simply not found in healthy cells. Human cells store their genome in double-stranded DNA, and use single-stranded RNA for transcription, but make no use of double-stranded RNA. Apparently, only certain viruses do, so the presence of dsRNA in a human cell should be diagnostic for viral infection, regardless of its sequence. In other words: see dsRNA, kill it!

Would that all viruses were that easy.