Sounds like Mr. Hambrick's logic here is flawed...
The logic behind these brain games is to help increase a person's capacity for learning, not to make them instantly smarter. How can a person become smarter by repeating the same type of information over and over? Along those lines with an example, how can one swiftly read through a book and instantly "learn it?" They can't without experience and training. When a person reads a book, they have to take time to logically think through the message of the book so that they gain insight as to understand what the author is saying. The logic here is limitless, but going along with the example of the book, these games help the brain to more swiftly break the information down into something more understandable for one to remember. Most of the games on Luminosity's brain trainer mobile app are geared at working faster with fewer mistakes.
I use Luminosity's Brain Trainer app on my iPhone and have done so for roughly 2 months. To me, it was well worth the $10 a year. Some of the benefits I realize I have gained of many are that I do a better job of having conversations with people in that I am better able to process what is being said to me and come back with an intelligent response of my own. I'm also more efficient at memory tasks especially at picture memory. One small example is I can write a note down on a stickie note and even if I can't remember exactly what I wrote, I can tend to pull a picture of the note in my head and read what was written on it. In addition, I no longer have to rely on my wife to remind me of most events (except for those I don't want to do and she makes sure to remind me). In math, I no longer get brain cramps when doing many arithmetic equations. I took statistics last year and only about half of it made sense. I had to break the work down into 15-20 min segments because I'd get a headache and have to stop. Now, I have no issues spending 2-3+ hours working with numbers.
Probably the biggest benefit gained has been getting rid of the headaches. This may also be from me working sudoku puzzles in tangent with doing the training apps. I wanted to get past the point to where I no longer had headaches and be forced to quit working my brain. I forced myself to keep doing both sudoku puzzles and the training apps through the headache doing a little more each day. Now unless I don't get enough sleep (less than 7 hours), it usually takes a few hours before I get these headaches and even then I'm usually able to continue working through them unlike before.
At the end of the day, it all boils down to what you do with this information. If you perceive that it's a waste of time, then it will be. It's also about getting past just being satisfied, and being motivated to learn. For me, these training games get and keep my brain in a state motivated to learn.
If you want to work on being "smarter" a book I'd recommend is "Critical Thinking: Tools for Taking Charge of Your Professional and Personal Life" by Richard Paul.