By limiting each team to one task per turn, Cranium prevents one team being able to overwhelm the other teams.
I.e. If a team was able to have another turn when they were successful at their first task, they could, in theory, keep winning tasks until they finished the game, without the other teams having a turn.
Dynamic: An interactive system or process, especially one involving competing or conflicting forces:
"The traditional nineteenth-century dynamic between the sexes had begun to erode"(Jean Zimmerman).
From: American Heritage Dictionary at dynamic
"Play dynamics" (dynamics of play) means the interactions between the people playing a game. I guess that in practice here it means something like "the situation arising from the rules of the game". It's the rules of the game that determine the dynamics, I think.