I'm afraid not. You cannot increase the height of a fully-grown spine by exercising. We're all aware that some people slouch and have poor posture. These folks could certainly be helped by exercises designed to make them stand straight, but the thrust of the advertisement you sent is to give cruel hope to adults with spinal abnormalities. Such conditions, which include scoliosis and compression fractures, are especially common in the elderly, who may suffer from osteoporosis or the normal shortening tendency that comes with age.
Most people can gain height by standing straighter and throwing their shoulders back.
Those with spinal abnormalities would be better off seeking medical advice and treatment. Most people die of heart disease and cancer between 50 and 65 than at older ages. Once you have reached your 70s, you have overcome a statistical hurdle. Some demographers have suggested that only relatively fit people live beyond 65. Of course, this is merely a statistical game.