If you want a room to control something without anybody installing anything, you have two sensors available. They are good at different things and the choice matters more than the software on top.
Microphone
What it gives you: one number — how loud the room is right now.
Strengths. Almost no setup. Works in complete darkness, which matters more than you would think, because plenty of shows put everything into the stage and leave the audience in near-blackout. Completely intuitive to an audience: nobody needs the rules of “be louder” explained.
Limits. One number is one dimension. You can build a tug-of-war, a meter to fill, a loudest-side-wins — and then you are largely out of ideas. It also picks up the PA, so it needs positioning that hears the room rather than the show, and it cannot distinguish four hundred people at moderate volume from forty people shouting.
Camera
What it gives you: a two-dimensional picture of where people are and how they are moving.
Strengths. Enough resolution to drive a real game rather than a meter. You can read position, posture, direction and timing — which means the mechanic can be about coordination rather than just effort.
Limits. Physical, and unforgiving. The camera has to be high enough to see past the front rows. Exposure must be locked or the lighting desk becomes a player. There has to be light on the audience. Each of those is easy to arrange if you know in advance and impossible to fix on the day.
How we are choosing
Camera as the default, because the ceiling is so much higher — and microphone deliberately kept as a real option for the rooms where a camera cannot work. A blacked-out room with no mounting position is not a rare edge case; it is a Tuesday.
The useful framing is that they fail in opposite conditions. Microphone struggles when the room is quiet and the PA is loud. Camera struggles when the room is dark and the lighting is moving. Very few venues break both at once.