I've played poker for play money. There's not as much pain when losing so there is correspondingly less motivation to exercise discipline, come to correct beliefs, or deal seriously with the difficult psychological situations. Learning to take those things seriously and perform under "survival instinct"-level pressure is the point of this training. You want the actions you take to imprint your habits and reshape them to be more rational over time and play money can't do that. See the post I linked to above for a longer explanation.

The football study you link to shows me that in cases where there's already a rich information market, real and pretend markets both mirror it well. That doesn't indicate to me that people wagering in the play money markets had a similar visceral experience or would learn the same lessons from failure or success. I strongly suspect they didn't -- and would bet money on it if I could figure out how.