One of the greatest risks in using games and activities in training is the activity doesn't connect in a relevant or purposeful way. I remember getting very excited to try a cool game and finding ways to insert it, regardless of its value to the program. That was a disservice to the participants. Doing so is one significant reason participants scoff at interactivity. But, when the activity is obviously, overtly, directly connected to learning, participants always engage. The most exciting game is inappropriate if it doesn't relate. As Thiagi says, all things can be taught through activity and all things should be taught through activity. Just choose activities that fit your learning objectives.
Training has a very specific purpose. Training is skill development and it requires application, practice, and feedback inherent in its design. If my intent is to convey a new policy, expectation, or concept, the best way to efficiently communicate is a memo, email, job aid, rubric, or meeting. If my goal is to change attitudes, my intervention is coaching, mentoring, or simple dialogue. Sometimes, these three types of interventions can weave together-- a new concept needs to be shared, then applied, while inspiring participants to embrace the change. In the end, be sure you know what your objective is and design the best interventions to meet that goal.
A good training program has a clear connection to skill development. And, that skill, once developed has a direct impact on either solving a business problem or enhancing the business in some other way. If the designer or trainer can't explain those two things, then why bother with the program. Politics? Legal compliance? Checking a box? Maybe... but these reasons have nothing to do with development.