The reduction of rest time method can be used to create greater muscular fatigue when you begin your next set. Because the muscle is only minimally recovered, it is much more difficult to complete the same load again with only 30s seconds of rest, as opposed to having 3-5 minutes of rest.
Another physiological benefit that reduced rest periods produces is metabolic stress, when giving the body less time to recover this increases systemic hormonal release and other muscle adaptations which can be a helpful tool needed to maintain our muscle mass without weights and barbells.
When we cannot add more load or weight to the exercise, reducing rest time is an excellent means of further taxing the muscle and introducing a new stimulus for hypertrophy and strength.
See below an example of Circuit Training, in which alternating between exercises which target different major muscle groups can allow us to eliminate rest time altogether without excessive fatigue.