It sounds perfect grammatically! However, for the exact sort of context you described above, we have words like "roughhousing" and "horseplay." So, we would use it like: "No roughhousing or horseplay allowed." You could also say, "Don't be rough or rowdy in the classroom." I personally would not use the phrase "dangerous game," because this would better describe a game in which the level of danger is high or in which the chances of getting hurt are high. A "dangerous game" might be something like jumping from tabletop to tabletop, or a race to climb a bookshelf--so if you are afraid your students would do this, maybe it is the most appropriate term! However, if you are intending to discourage young students from wrestling, running around and chasing each other, or other similarly disruptive behaviors, "No roughhousing or horseplay" might be more appropriate. Hope that helps!

In my years of learning in U.S. classrooms, I found rules more specific and not left to interpretation by the child. For example, no running during class, no talking during class, no eating during class, etc.