At first I thought this would be easy so answer, but thinking more about it, I am actually not sure. I'll take a stab at it. I think it has to do with the air temperatures around it and all that gravity that Earth has going on. When we heat up the air inside a hot air balloon, it rises higher up because the air around it is more dense than the air inside it.

So I believe it is the same thing with fire. Each individual particle is really hot and as it heats up it wants to expand. There's all this cold air around it, so it is easiest to go upward. Sure there's some cold air above it too, but the gas from the fire doesn't care about those because it's hot as fuck and needs some room to breathe. Easiest place to go is up because all the air around us is just a big column of gas, so it would be less dense higher up because there's less air sitting on top as you rise.

In microgravity it is a sphere because that is the most efficient way to distribute the energy when there's nothing else to effect the system. If there isn't regions of higher pressure and lower pressure, then the reaction should be more uniform. Until something happens that causes the reaction to lose its symmetry. This is shown in the gif towards the end when the fire begins to shoot downward. I'm sure /u/Popular-Uprising- knows more about it, but I'm thinking maybe that lighter sphere could be carbon monoxide or whatever gases fire make. So the little jet of fire begins to shoot downward because there may be some difference in pressure in that area compared to the rest of the sphere. Then it keeps shooting in that direction because the sphere is now like an untied balloon. The hole has been opened up so it is a lot easier for the gas to go through the hole that was already made than to go through the walls of the sphere.

At least that's what I reasoned. I just checked my grades today from last semester and found out I actually passed Physics so I'm feeling pretty pumped. Hope that helped and was close to the real answer.