Er, definition of art must by default leave "intention" out of the picture. You can't know if the person who made the thing, or if it even WAS a person, had any intentions of making anything. Or if it was actual design, or accident.
You can find something designed by an aleatory algorithm totally beautiful and artistic, so where does that leave "art?" Really now, art is from the view of the observer and pretending it isn't is writing yourself into a corner. If you observed the result of said algorithm WITHOUT the knowledge that it wasn't someone that consciously designed it, and instead the person who wrote the algorithm did it as, say, homework for a class with zero interest in it being art or anything like that, then what?
This is the reason these definitions fail:
"Art is any intentional form of human expression."
Not really as my example above shoots a rather huge hole in this as you can't tell intention just by the finished product. You need extra information that may or may not be available and everything else is assumption.
and
"Art is a pattern of sensory input designed to alter the mental state of a person who perceives it."
My example above also shows that "design" can be entirely accidental or aleatory. That you perceive an illusion of "design" in things isn't false, but it doesn't mean actual design (by somebody) must be necessarily involved. It can be an accident, and again this requires information that may or may not be available. Design assumes intention and you may or may not be able to get this information from only the finished result.
And it creates the retarded scenario that finding out something behind the previously thought work of "art" makes it suddenly not "art." Which would be the logical consequence of such definitions, and it really makes absolutely no sense as information ex-post-facto can't negate the experience you already had.
Hence, saying X is or isn't "art" is nonsense, since it's only a personal opinion. Others may share it, it may be part of culture, but it's simply a personal judgment. You can't objectively state X is art, you can just explain your reasons, but they are subjective.
And that's how you can tell these arguments about games being or not being "art" are made by people who have, often, no real understanding of modern aesthetics and modern art history. In reality there's so much stuff out there that you'd find extremely conflicting opinions on it being or not being "art" that games are kind of insignificant in comparison. After all, people have been arguing about this for a long, long, long, time.