Space

Quite a bit more complicated with important distinctions. The biggest differences are where the combustion is occurring.

So from what I understand, previous rockets shot exhaust out the back in a cone shape. That essentially sprays the exhaust out kind of like a shotgun.

Not really. In a bell nozzle engine (which is the traditional rocket engine everyone knows about), the combustion is happening at the far inside of the bell, and the bell is shaped so that all the fuel is burned inside the bell at a specific air pressure. The thrust is provided by the burned fuel which is traveling at high speed. If the air pressure goes down (because your rocket is now higher), you're losing unburned fuel out of the bell, and its providing no thrust. This is the limitation of bell nozzles.

Example. These are the essentially the same rocket engine. The one on the left has a smaller bell (called a skirt) because its sized for air pressure at sea level (which is high). The one on the right is size for the vacuum of space where there is essentially no air pressure.

Wouldn't it be great if there was a single engine that worked great at sea level and equally great in vacuum? That brings us too....

This adds a donut shaped ring of plasma around the tip of the cone which focuses the exhaust into a tighter stream, more like a laser, improving thrust.

Not exactly. What you're describing is called a regular ** "aerospike" rocket engine**, which some designs do have a cone in the middle. What makes the shape so useful it that air pressure pushes the combustion against the cone (spike) at the perfect degree at sea level and in vacuum so that it is very efficient for burning all the fuel without loss.

The problems with aerospike rocket engines is they are VERY heavy, and that cone in the middle gets CRAZY HOT and has a tendency to melt down while the rocket engine is firing

Neat!

The "neat!" is the engine the article is talking about which you haven't described yet. This would be the Rotating Detonation Rocket Engine!

To our slow human eyes it kind of looks like a regular aerospike, but if you slow motion it, you'd see that the flame isn't constant all the way around the cone. A RDE engine has single flame that is racing around the circle and contained by shockwave from the previous combustion.

This also means the cone in the middle stays much cooler, which means it can be made much lighter and not melt down.