I'm going to throw out a couple of theories here, but don't know if any of them are actually correct. I'm just taking a shot, based on my (limited) knowledge of physiology.
(1) When you walk (or perform any kind of exercise,for that matter), your blood supply is diverted to your extremeties, to provide nourishment for the muscles as they engage in physical activity. Extra blood in your fingers would indeed cause them to swell. However, this theory doesn't have any explanation for why this doesn't happen to you during other forms of cardio. My next theory is probably more likely...
(2) When you walk, you are swinging your arms back and forth. There is a centrifugal motion occurring here, and referring to our knowledge of physics, centrifugal motion causes the bodies in motion to tend toward the outside of the arc. The outside of the arc, in this case, is formed by your fingertips. The muscle, fat, and bone tissues of your arms can't physically move toward your fingertips... but your liquid blood can. And so, with every swing of the arms, your blood is being forced toward your fingers by centrifugal motion, causing them to swell. You don't get this effect with other cardio, such as step, because your arms are usually doing something besides swinging back and forth, so the blood is not being constantly pushed toward the fingers.
Like I said, just theories, don't have a clue if they are correct.
