Almost all group sports promote teamwork. But you must be very careful in choosing your group sports for team games. Because how you win the game, not just how you build the team, is a metaphor of how you want people to achieve corporate goals.
You do not want a divided workplace. But every time you choose games that make one team winners and another team losers, you are practically aiming for at least half of your team to become losers — and when you process the result of the games, you cannot simply say that one team did not win because their members have less teamwork.
To be number 1 in your industry, you do not have to kill your competitors.
To be number 1, you have to delight customers that they will choose you every time. You do not set your eyes on your competitors all the time. You set your eyes on your customers and communicate constantly with your team members to deliver excellent service as a team.
You can choose games that will show them how they can be quick and reliable in serving customers, not in killing competitors. In real life, you will not die when you make mistakes. You can use your mistakes to enhance your skills and serve your customers better.
If you have teams like customer support, marketing, production, and operations, you will miss team building a hundred miles by choosing a game that make other team members losers. There are better alternatives to killing each other in a game.