The main issue is not how you can incorporate your ideas into the activities rather, it's what activities should you use and adapt to stress the importance of your ideas.
Focusing On The Main Points
You are not adhering to any copyrighted works, when you employ a game or other team building activities. What works for one team may not work for yours especially considering the many different industries that use a team building system. Trainers and managers are advised to know their team and to develop an education course the benefits them, as opposed to a system that benefits others. If an activity works for IT computer employees, does that mean the same activity will work if you're coaching a little league team? Maybe you appreciate positive aspects of a certain activity. In that case, then borrow the concept and adapt it to your circumstances and your team. Eliminate the unnecessary or confusing elements and focus on the main points you are trying to teach. There may be rules to a game or activity that conflict with what you're trying to accomplish. In that case, it's better to create a new game that quickly speaks the point, than try to figure out a complicated way to apply the activity and all its technical rules.
Think of ways to apply a team building activity to a particular industry and to your specific team members. If you notice that your team members share many characteristics or have a natural enthusiasm for something (Money! Sports!) Then incorporate those motivating factors into the scenario. If you are planning on a quiz game, then include tough questions that are relevant to the team whether it's questions on business, sports or entertainment.
Pulling The Strings
It is also acceptable to strategically assign roles and game features so you can test various members of your team, or even to produce a desired effect so you can emphasize a point.
It's important to keep all of your team members challenged, as much as possible. Everybody wants to excel, and certainly some members will proceed faster than others. You may give the more active members plenty of things to do and be successful, and think the team building effort is going well. But what about the members who are not performing as well? Can they still be worked with? Nobody likes to be neglected and part of being an effective trainer is helping team members to excel at their own comfortable pace. In cases like this, devise an activity that assigns members different roles based on their skill and experience. Find challenging work for everyone involved and make sure the entire team is playing to their best abilities.