... but we already knew that not all life relies on oxygen.
Obligate Anaerobes are bacteria that actually require an absence of oxygen in order to grow. Of course, there is oxygen within the molecules in the microorganisms, but environemental oxygen that we are exposed to can actually kill them for various reasons.
What this microorganism can do is incorporate arsenic, almost as a replacement for phosphorous, into its DNA and other molecules that are required for life (note that they are in the same group in the periodic table). This means that the organism either takes up or processes the arsenic differently to what other cells can do.
In terms of aliens, the Mail is overstepping the mark (as usual) by calling it "alien life on earth". It shows that organisms can in fact develop methods of processing arsenic, and this does have implications in the search for extraterrestrial life as well as in the field of microbiology, but it doesn't mean they've found aliens. They've just found an organism with a new biochemical pathway. But I suppose that doesn't make for an interesting headline.