"Functional" and "performance" are two relatively subjective terms often used to describe exercises and training like the moves included in the video above. They are of course relative to your goals from training but semantics aside, there are commonalities among many of these kinds of exercises.
They not only serve as a gauge of what the benefit is but also give us insight into the pre-requisites that clients should meet before graduating to more advanced moves.
Often times clients and even we as trainers want to skip steps and go straight for the sexy stuff. You can't build a great house on a weak foundation so fight your urge to go straight for the roof. This doesn't mean we aim to handcuff clients from movements and variety but need to progress them accordingly.
Here a two major things to keep top of mind with this type of training:
1) Core Stiffness
The true function of the core musculature is to create a stable foundation for movement and force transfer. This doesn't mean the core should never move and you can't train power moves like medball tosses, etc. It does mean that using exercises that challenge core stiffness in all planes of motion will have a strong carry over effect in performance across the board.
Exercises like the overhead split squat pictured above require massive amounts of core stability with the weight loaded onto one side of the body (off-set loading). Other moves like the TRX Halo purely look to challenge our ability to hold a stable tight position. Clients lacking in core stiffness may not only be underperforming when they move onto power movements but they also present themselves for a greater risk of injury.
2) Complex Integrated Movement Patterns
This doesn't mean you need to stand on a bosu ball and pat your head while rubbing your tummy. It just means that more advanced performance moves can be more technical and should be broken up.
This may not seem as obvious for simpler movements like a squat jump but the moment you leave the ground the demands multiply. Normal squatting requires no landing patterns so just because someone is used to squatting doesn't mean they are ready for max vertical jumps. You must first teach them to land appropriately. You break up the pieces and allow them to improve before throwing it all together at once for a maximum effort training attempt. Another example would be the overhead split squat described above. A client should be able to complete overhead weighted carries and weighted TRX split squats separately before combining them together in one movement.
There are a lot of variables that go into programming and progressing clients. These are just a few concepts to keep in mind when it comes to building in challenging variations and more performance based training. All exercises present a risk-to-reward ratio and with the right training we are able to minimize those risks for the best return.