It was hard to see this rule back in the day when TV's didn't have a 16:9 aspect ratio, but it's easier to see that the rule of thirds plays an important role in cinema. There's a bit of psychology behind it too.
One of the first things you'll learn about the rule of thirds is the placement of objects inside the grid. The grid is lines that make up a 3x3 grid inside the frame. The parts where the lines cross are the places where our eyes look for information first. Let's look at a coupel of examples.
This is your basic interview shot. Of course, your eyes would go straight to the woman's face since she's talking. There's plenty of room around her to make the shot feel less chaotic even though she's standing next to a helicopter incubator. If she was standing next to a background with more things to look at, the shot would have been unusable. Since this is a hospital room, your mind already expects it to look like this so your unconsciously disregarding how messy the background is. Let's look at another example.
This is another interview style shot. In this one, the shot is set up perfectly. Just enough head room and pleasing colors around her to separate her and the background. The object on the table behind her isn't distracting but you'll also be looking at it once she starts talking about it.
The point is, the people and the objects in the frame work together to compliment each other. At or near each point that the lines cross, your eyes will go to there to see what is there. This is where another tactic is being used. The space in which is not being utilized with an object or another subject is called leading. This is where you put your subject on one side of the frame and the object of which they have their attention focused on the other side of the frame. In the case of the interviews, their focus is on the interviewer. Even though you never see the interviewer, you know that they are there and it feels more like they are having a regular conversation instead of watching a public service announcement that you would see on TV.
The rule of thirds can be seen on any TV show or film. The next time you watch something, think about the grid, you may start to notice how strategic these filmmakers are.