You can download the model JSON from the editor itself. Select the JSON and click download in the inspector panel on the right.
This should download a zip with the model JSON, the materials, textures and the mapping JSON file as you have shown from the screenshot above.
This package includes the JSON for the model, JSON for the material mapping to the mesh instances in the model and all the relevant textures used for the materials used.
You can host those files (keep the directory structure) somewhere and load them at runtime as shown here: Load 3D models at run time from a PlayCanvas application