Alright... Speaking as a graduate student in physiology with a heavy background in genetics, lemme make clear:
That rabbit/human hybrid was the infusing of human genetic material into a rabbit egg cell that had its genetic material removed. There was no fusing of rabbit and human DNA. No "Furries," which I understand to be rabbit/mouse/whatever humans. In fact, it probably would be much easier to create a "Furry" through prosthetic bionic ears/tails than through genetic manipulation.
The research going into creating pigs/mice with human cells and body parts can sound grotesque and unneccessary, but it's all part of helping us understand development and genes which regulate when/where body parts are grown. This in turn leads to more useful applications such as growing livers, hearts, lungs in animals for human transplant.
But enough on that... just so you don't have any misconceptions on becoming a biology major, let me fill you in on what you CAN'T do. Not now, not for another 20-30 years at least.
1. You cannot, through viral treatment or what have you, modify a fully developed individual's DNA. This means no growing cat ears, tails, extra limbs, etc. Once you pass the single cell stage, there is no viable option (at this time) to modify your developmental pathway.
2. It is not a simple thing to simply "grow" a tail or ears. There is no single gene for tail, or ears, or whatever. These limbs, body parts, are all part of a developmental program based on thousands of genes.
3. You cannot simply "mix" genetic material of different species together. Chromosome number for species is different, not to mention the inability.. oh damn there are just so many things wrong with that concept, just forget it. So that means no Ligers or Tigons or whatev.
4. Mutations, either by radiation or mutagenic substances, won't alter any organism besides giving it cancer. See 1 above. Mutations are by their nature random, and so the only way, say, the Fantastic Four came to be would entail the cosmic radiation (which exists, and is a big problem for astronauts,) creating the same mutation (not just deleterious ones like most are, helpful mutations) in every single cell of that human's body.
So you're right kuwoobie, its not that simple. The authors of that article failed to mention that a chimera in scientific terms simply means the fusing of two cells of a different species together. I think (i'm not certain... i work with plants and plants are much better to work with than animals) that in the case where there are two nuclei with different genetic material in the same cell, one is aborted or the entire cell aborts. Most of the successful examples of creating a chimeric cell are when the genetic material of one cell has been removed beforehand.