You seem to be getting hung up on the fact that Draper isn't actually a startup founder pitching his own product to investors. That's almost completely irrelevant. He is definitely pitching the product. In this case, he simply happens to be pitching the product back to the company who made it.
Pitching and advertising, while they have their differences, are fundamentally about the same thing: getting people to believe a product can make their lives better. If, in addition to tossing out numbers, you can make your potential investors believe you know how to connect with your market and truly understand their needs, so much the better. It doesn't have to be in tear-jerker form like Draper's presentation: it's about knowing how to frame the product.
And sure, it's a TV show, but it happens to be a fairly exceptional TV show built on a great deal of wisdom about what makes people tick. Don't throw the baby out with the bathwater.