Looking at the paper itself, we find that they prepared the stem cells to have myogenic (muscle-specific) properties. They first injected stem cells into the irradiated (which kills muscle stem cells) muscles of immune-deficient mice. This resulted in tumor growth (teratoma - a stem cell derived tumor, where different kinds of tissues are spontaneously formed. Growing in a muscle environment increases the chance of muscle tissue formation.). The tumor cells, which expressed muscle-specific markers, were isolated from the other tissues and then used for regeneration of an injured muscle.
In their teratomas they checked for cells expressing α7-integrin and vascular cell adhesion molecule-1 (VCAM-1), which are markers expressed in satellite cells (muscle stem cells). These factors were expressed in about 10% of the fraction that did not show any hematopoietic and endothelial markers (meaning: there were a lot of other tissues formed as well). They also showed expression of Pax3 and Pax7, which are muscle-specific transcription factors, important for differentiation of myogenic progenitors. These cells were therefore already muscle-specific cells before they have been transplanted for regeneration.
The researchers did, in fact, do in vitro and in vivo differentiation experiments. For in vitro differentiation they subjected their muscle-marker expressing cells to a myogenic medium. This mimics the muscle environment and enables cell differentiation signaling. Here is an example protocol how this can be done. Then they transplanted their muscle stem cells into a muscle and they also managed to differentiate in vivo and regenerate the injured muscle.
The entire process of pluripotent stem cell to muscle cell differentiation can be performed in vitro, but seems to be tricky (1,2). Medium factors or genetic activation of transcription factors can activate different steps in the differentiation cascade.