No, sorry, that's not the gain medium. If you want to get REALLY technical, there are 2 gain mediums in your diagram. In these DPSS systems, it's like running 2 lasers: You provide electrical energy to pump the 808nm diode (the materials in the 808nm diode provide gain when pumped with the electrical energy), so the semiconductor material in the diode is a gain medium.
Then that light is focused (that's the Pump Focusing lens) into the 2nd gain medium, which is the Nd:YVO4. The Nd:YVO4, getting pumped by the light from the 808nm diode, then acts as a gain medium for the 1064nm light.
Also, with how these things are built, the gain medium in both cases here is the same as the optical resonator: the semiconductor chip in the 808nm diode is the gain medium and its 2 ends form the optical resonator. Same the the Nd:YVO4, the crystal is the gain medium as well as forming the optical resonator. For the "mirrors" of the optical resonator, they just use the facets of the crystal. The semiconductor/air interface forms the mirrors on the diode, and the crystal/air interface of the Nd:YVO4 crystal forms the mirrors for it. In practice, sometimes this simple interface is enough reflectivity, but often it's preferable to put simple thin film coatings on the the ends of the semiconductor or the Nd:YVO4 to increase reflectivity. In that case, the facets are still the mirrors, but the mirrors are enhanced by the thin film coatings.