Is this study/article scientifically valid.
The study you refer to shows that a measure of brain white matter connectivity, called diffusion tensor imaging (DTI) shows increases in structural connectivity between brain areas that have been previously implicated in reasoning and other brain functions.
The news article goes on to make additional claims, not made in the paper, that this result means studying for the LSAT improves reasoning overall. The study itself does not make that claim, and they did not test reasoning besides measuring LSAT performance. Therefore, you cannot conclude from this work that studying for the LSAT improves performance on anything besides the LSAT, only that studying is sufficient to make detectable changes in brain structure.
I would certainly say it is plausible that studying one set of tasks, like studying for the LSAT, would cause improvement in related skills (certainly this assumption is the basis of a whole lot of pedagogy), but that certainly doesn't mean it is the best way to improve or that it is special compared to other types of study.
Note also that the participants in the study were involved in a particular training program and the results may not generalize to other forms of LSAT preparation.
As a side note, it is always important to read original research articles before taking news at face value. Even the researchers quoted in a news article may not approve of how exactly they were quoted. The news process is subject to sensationalization and the qualifying language that scientists frequently use may not reach the final edits.
Mackey, A. P., Whitaker, K. J., & Bunge, S. A. (2012). Experience-dependent plasticity in white matter microstructure: reasoning training alters structural connectivity. Frontiers in neuroanatomy, 6, 32.