Mastering the regular landmine lifts instantly makes all other strength and performance training better. It requires the ability to create full body tension from a standing position, which is more "functional" for most athletes.
The next progression is to create a more reactive and explosive environment. The ability to decelerate, stabilize, and re-accelerate is key for optimal performance.
To do the athletic landmine, start with a regular landmine "full contact twist" before you create a forceful rotation and perform a side shuffle movement starting from the core and hips.
The bar coming down to the side will load the hips and core muscles, much like a coil. The purpose is to quickly and precisely stop the barbell/weight, before re-accelerating it to the other side.
Even though the exercise isn't super advanced, safe execution requires a strong core and good timing. Start light and make sure you have the regular landmine move under control. You don't want to go too heavy here. You won't get max power output with the heaviest weight.