My smoke simulation looks nothing like in the video. It rather looks like something from a 1996 video game.
These are all pretty much the default settings (see below). Help :P
I can get a bit more detail that way, at the cost of a lot more computing power/time, but the flame still burns white hot compared to the more orange'y flame shown in the video. The fire show in the video also looks to be behind the smoke, and in my image it kind of just blends with it. It's not that importan though, as Blender 2.8 has a very different smoke look from my 2.79 :)