UPDATE:
After installing the lasted GPU drivers (Nvidia Studio Drivers) I manage to solve the problem on my desktop computer (It has a GTX 1070). Now I can watch the video on YouTube with no issues. Still, on my laptop that has an 2 GPUs (Intel HD Graphics 4600 and NVIDIA GeForce GTX 950M), the problem remains. So probably the issue has to do with the GPU and drivers and this is why some people experience the video with clipped colors and others don´t. This is why the problem with the colors is gone when you turn OFF “Hardware Acceleration” in your browser settings.
It depends on the drivers and if your GPU can handle HDR video.