Klepek offers the clearest explanation yet of the two-tiered gameplay. Defeated enemies are sent down to the bottom screen as squares in a "Planet Puzzle League-esque" puzzle game. In addition to the benefits provided by successful combos in the puzzle area, it is important to clear these squares quickly, or else they will go back up into the platform world as enemies again.
As for those combo benefits, Klepek gave an example: a lightning attack earned by pulling off combos, which allows Henry to damage an enemy severely. We think somebody pulled off a combo of John Madden-shaped blocks that afflicted us with the status of "being interested in an EA game."