When studying the video clips of collisions on the field, it becomes immediately clear that the motion of the two players after a collision is much more complicated than the motion of the carts. The motions of the CMs of the players and the carts immediately after the collision is similar, but the carts subsequently move with nearly constant velocity, while the players slow down quickly or fall down. There are two main reasons for this difference in motion.
Why does it get so complicated?
Players are extended objects, not mass points. Extended object can have translational and rotational motion. Any motion of an extended object can be viewed as a combination of translational motion of the center of mass and rotational motion about the center of mass.
A foam square has a blue LED near its CM and a red LED near its edge. If we toss the sponge we can easily observe the parabolic motion of the CM and the rotational motion about the CM.