Problem to apply project mapping

That is the tutorial that I thought it was and I've answered the very same question before. Here's the problem. In spite of the huge number of views, the tutorial is pretty mediocre. The presenter did not present the most efficient workflow and he left out a bunch of critical info that has caused you and others that I have helped some problems. One of the biggest mistakes is Warp Stabilizing a shot before you run Camera Tracker. He was very lucky that did no completely screw up the Camera Tracking. If you need Warp Stabilizing that should be applied to the entire comp after all of the compositing and effects are added. That is the only way to get a composite to stick properly to a warp stabilized shot.

The choice of a light source left out critical information and that is almost certainly the cause of your problem. It was the problem for a few of the other people I helped when they tried to follow that tutorial. Scaling the 3D copy of the footage used as the gobo is a bad idea and throwing in Corner Pin is to fix rotation and scale problems another way to introduce errors. Even the Camera Tracking section left out a critical step of using Advanced Analysis checking the tracking error estimation, and setting an origin and Ground Plane. The tutorial is based on a good idea and a common technique that has been around for a very long time. I did a tutorial over at Creative Cow right after AE introduced 3D layers to After Effects in AE 5.5. Here's the tutorial I did in 2002 - about 17 years ago: Using Projection Layers to create gobos and projector effects. Unfortunately, the images and the project files are long gone. 

Let's talk about adding the light first. It must be a Point Light, Color must be white, Intensity must be 100%, Falloff must be set to None, Cast Shadows needs to be on, Shadow Darkness must be 100% and Shadow Diffusion must be Zero. Shadow Diffusion is the most likely source of your problem. The size of the Shadow Map (Comp Settings>3D Renderer>Options) can also cause some problems, but I think yours us just Shadow Diffusion.

Let me talk about adding the Freeze frame to a copy of the footage layer to use as the gobo (projector image). Adding Freeze frame may be an OK idea but it complicates things and in the long run, it is going to slow down your render. A more efficient option is to save a Frame as a File using the Composition Menu. This not only gives you the opportunity to do a little cleanup in Photoshop if necessary with the Healing Brush or other tools and the default file name will have the timecode or frame number from where you took the frame. 

Now let's talk about setting up the light and the projector. Holding down Shift to Parent the light to the camera is the most efficient way to get there and that is OK. Turning off Parenting as soon as you do that is also important, but if you select both the light and the 3D layer you are using for the gobo (something that you put in front of a light source) and then Shift + parent them both to the camera. This will put both at the camera position and get you set up for the next step. With both the light and the gobo layer at the camera position and at the same orientation you should select the camera layer, press "aa" to reveal the camera properties and copy the Zoom value. The next step is to reveal the position property of the gobo layer. Because it is the child of the camera the position will be 0, 0, 0. Select the Z value by double-clicking and paste the zoom value of the camera. This will move the gobo to exactly the right position and square it up to the camera perfectly. Then select both the Light and the gobo and remove the parenting. There is no need to scale the layer, not need to try and rotate it into position, and no need to add the corner pin. Using the Zoom value for Z position after parenting will always move the gobo layer into perfect alignment with the camera.

The rest of the tutorial is fine, but you can see how leaving out the details of the light settings and explaining what they do cause problems.

If you still have a problem try revealing all modified properties of all layers. Press the "u" key twice, then check the light layer first.  You should only see the position property and Cast Shadows showing. If there are any more properties visible reset them and the image should be sharp. This is what the comp should look like with all modified properties of your layers revealed. Notice the Origin layer is set to a guide layer and the grid effect is still turned on so I can verify the Camera Track is good. Note the expression for Position in the footage layer to keep the layer centered in the comp frame. I always do this when I use Camera Tracking.

I saved a bookmark for that tutorial just in case I need to find it again to help someone else.