Goodness. That Webster's is the only definition of this term is unacceptable.
Webster's is basically right, but in practice the word is almost always used in terms of computability. A problem is said to be intractable if it would an unacceptably long time to complete. Some problems are tractable (i.e. do-able) in small cases, but become intractable as problems get large. The analysis of how quickly various algorithms move from tractable to intractable is what a lot of computer science is about. In fact, you could say that the whole NP-Completeness discussion is fundamentally about which problems are tractable and which not, and how quickly various problems move from one side of the line to the other.
You can raise the argument that intractability is relative. You can boldy thrust forward Moore's Law - like a child that's made a macaroni bird in art class - but if you do, you're not getting it. Intractable is bigger than Moore's Law. Intractable is like, thermodynamics big. To say something in intractable is (unless the statement was meant as hyperbole) to say that if you built a computer using every subatomic particle of the universe, if you used the minimum possible energy to store states, and if you captured the energy of every star at the moment it went supernova in order to power this computer: it would still take a very long time.
Intractable is badass. Intractable is when a problem gives you the finger on both hands. You wish you were as hardcore as intractable. Now you see why Webster's just doesn't do it justice.