in this tutorial (https://www.youtube.com/watch?v=ZJWiscCnblw) I was wondering how the artist was able to ‘paint’ on geometry on the skin of the creature using what appears to be texture painting… I am fairly new to this concept. Someone please enlighten me 
It’s not a tutorial and there is no painting in that video. Perhaps a wrong link. In case not, it uses viewport display modes and I’m guessing the final turntable wasn’t rendered, just captured the viewport with opengl render.
Next time include a timestamp to the relevant part in the link.
If you look carefully, Senor Gordillo is in Sculpt Mode. The button is on the header of the 3D View, same one that shows whether you are in Object mode or Edit mode. You can find a variety of Sculpting tutorials on Youtube.