Most Team Building Activities will put people under time pressure and therefore force them to prioritise tasks. This in turn teaches people to prioritise how to get more done in less time. Further it also teaches skills such as goal setting and other key time management techniques.
Effective communication is critical. Therefore every team building activity will either succeed or fail based on the quality of communication between team members. As a result it is important that they give great feedback on how effectively your team communicate, listen, and work together.
Most team building activities are like a mini project and will require people to delegate clear roles and priorities. However they can provide great feedback on the leadership and management of key individuals in your team.