You could show the same thing by relaxing those assumptions. It would just require a lot more algebra. The key insight is that, holding everything else constant (which is done in the lecture), weakening your accuracy to one side increases the probability you target that side.
Game theory doesn't become computationally intensive until you reach mixed strategies, which start about half way through the first chapter. (If this comment is referring to the PDF preview on my website, the PDF only contains the first lesson.)
When I started making the videos back in 2009, my concern was just showing how to solve games. Details were details, especially since your average YouTube viewer does not have much an attention spam that lasts past five minutes.
But you're right, the other things are important. I eventually get to them in some of the later (and longer) videos, I talk about them in the textbook. The first lesson is a free PDF on my academic website wjspaniel.wordpress.com, so you can check it out if you are interested.