If we're willing to expand the definition of life, e.g. to accept some type of self-aware computer as alive, then we'd have to tweak the definition, such as it is, and then we're no longer talking about "life" as we think of the word today.
I guess people often wonder about other biochemistries. As far as I know, from a semester of undergrad astrobiology, we don't currently consider those very likely. Silicate chemistries were speculated for decades, but the chemical dynamics just don't tend to work out. The other main idea was ammonia as solvent, but that'd be hardly exotic, and the current thinking is that biochemistry would be entirely too slow at the temperatures where ammonia is liquid.
The wilder ideas, like high energy chemistries on the surface of neutron stars only ever appear in science fiction. (Excepting the odd paper from the seventies, but that was a strange time.)
Maybe people will accuse me of a lack of imagination, but I think it's telling that these threads are almost always mainly the home of comments shouting the word "quantum" like it means something, or getting their information from Mass Effect.
I do think it's an interesting question whether we'd be able to recognize other types of intelligence, but I am pretty sure we'd be able to recognize other types of life.
(By the way, the article seems to be mostly about whether we'd recognize alien life seen through a telescope, but that hasn't deterred speculation about other kinds of life in the thread.)
Source: I actually studied this in college, for a bit.