The science on this topic is somewhat inconclusive. The latest Cochrane review of all of the research on the subject concludes that the evidence is not strong enough to merit widespread use, but there are probably some benefits including weight gain.
The original study, Massage of preterm newborns to improve growth and development, was published in 1988. The author, Dr. Tiffany M. Field still a professor and her lab is called the Touch Research Institute. The website for her lab repeats this finding on the home page. She apparently still believes her original finding, and is still doing research in this field.
In the years since publication, the study has garnered 118 citations. These citations are part of post publication peer review by other research groups, which is the ultimate test for scientific concepts.
These two papers are follow up studies that Dr. Field worked on. It is great that Dr. Field can repeat her own work, but I will be more convinced if someone else can replicate her findings.
In 2003, Dr. Field wrote a review paper about Preterm infant massage therapy. She describes 4 replication studies, done by other people, that followed her method and got very similar results.
She also briefly cites a Cochrane review of the subject from 2000. Cochrane "produces and disseminates systematic reviews of healthcare interventions and promotes the search for evidence in the form of clinical trials and other studies of interventions." They are a third party who's mission is to summarize the evidence so that practicing doctors can quickly make evidence based decisions. Both the 2004 Cochrane review she cited, and the the latest Cochrane review of the subject (published in 2015) say that there is some evidence of benefits but the evidence is not strong enough to support widespread use.
Benefits of massage ... for preterm infants are: improved weight gain, decreased response to pain, and increased interactions with parents. However, the few studies use different interventions related to timing and number of massages, and the outcomes vary among studies. There is not enough evidence to support the use of massage for term and preterm infants, but massage may be considered on a case-by-case basis.
The Cochrane reviewers are more critical of the quality of the evidence than Dr. Field is. They cannot wholeheartedly recommend it, as I am sure Dr. Field would.