I’ve seen a number of discussions here – as well as the lecture itself – mentioning that the Boolean modifier can be somewhat… unstable/unreliable. Perhaps things have been improved in Blender 4, but I seem to have no issues with simply adding a cube over the area that I want to remove, targeting that with a Boolean modifier attached to the wall object, and then hiding the cube itself:
So again, perhaps things have improved since the time of this recording and my own follow-along with Blender 4.0.2 (Or perhaps there’s a slight difference in my wall geometry that is turning out in my favor 
)? But in either case, I do tend to feel more comfortable using non-destructive modifiers if possible.
That said, I did play around with a potential third approach that could lend itself to modifiers and the Knife Tool.
Given the destructive nature of straight-up deleting vertices, I found that a nice middle-ground solution between this and using Booleans is the Mask modifier.
I started by cutting out faces with the knife tool as the lesson shows. But then instead of deleting them, I assigned their vertices to a Vertex Group, targeted it with a mask modifier, set the target to Inverse, and then tweaked the threshold a bit:
This video also contains a good demonstration of what I’m getting at: https://youtu.be/YVUkiXTJtZc?t=121
At this point, for our wall here, it does still revolve around a lot of knifing and geometry destruction – but I think it’s handy technique to know about regardless 