Vertical integration is a training system popularized by Charlie Francis. It is nothing more a way of blending together training components throughout the training plan. The key concept is that a training component never gets removed. It only gets de-emphasized. A thread of that quality always remains in the program.
The reason this becomes necessary for team sport athletes is that they need many different qualities for their sport. A soccer athlete needs, agility, maximal speed, acceleration, explosive strength, etc. Instead of training each of these qualities in separate blocks, we train them all at the same time but emphasize one or two qualities while the rest are trained with a minimal volume. This allows us to devote all our energy to developing a certain quality while maintaining the other qualities in the background.