A BMP (DIB) image is composed by a header followed by uncompressed1 color data (for 24 bpp images it's 3 bytes per pixel, stored in reverse row order and with 4 bytes row stride).

The bytes for color data are used to represent colors (i.e. none of them are "mandated" by the file format2, they all come from the color of each pixel), and there's a perfect 1:1 correspondence between pixel colors and bytes written in the file; thus, using perfectly chosen colors you can actually write anything you want in the file (with the exception of the header).

When you open the generated file in notepad, the color data will be shown as text; you can still clearly see from the header (the part from BM to the start of the text), that is mandated by the file format.

In my opinion this video was done this way: first the author calculated the size needed for the bitmap, and created a DIB file of the correct size filled with a color that expands to a simple pattern (e.g. all bytes 65 => 'A' ); then replaced such pattern with the "payload" code, as shown in the video.

Notice however that it's not impossible to hand-craft the whole thing with notepad - with the color chooser dialog, an ASCII table and a basic knowledge of the DIB format it can be done, but it would be much much slower and error-prone.

More info about the DIB format