Is the “Brain Song” being advertised as able to enhance memory by stimulating Brain Derived Neurotrophic Factor after 17 minute listening sessions, truly effective and superior to other, routine, cognitive exercises, such as listening to music, playing an instrument, tackling demanding creative decision-making tasks, etc?

As you are seeing intuitively, this is not a magic potion that uniquely can stimulate the brain in a positive way to bring about symptomatic improvement or prophylactic benefit for maintaining high-level cognitive function, it is one of many, many, things. It is simply the case that it has effectiveness for a short-term neurologic change on the level of physiology, the current biochemical milieu, of the brain, which can be measured in conjunction with a laboratory experiment that lends itself to gathering interesting clinical data under controlled conditions. The list of things you mention is far from complete. It is true many people live lives lacking in positive experiences that stimulate the brain to go into a regenerative mode, much akin to the way physical exercise energizes and rejuvenates the physical body with some carryover to the brain as well. So we see this can be a useful adjunct for some, but it is not a universal answer, nor the most profound way to help stimulate the brain to provide a beneficial boost to focus concentration and memory. For those who are drawn to this and adopt it as a regular practice, there will be a positive return that might be noticeable, but not all will be a good fit. It might not be something they will keep doing and that is the commonest drawback of using such adjuncts. Even when they are likely to be useful they will need to be implemented on a regular basis for enough time to accumulate a series of resets and readjustments before there is a tangible persistent benefit in function.