Do short workouts like jump rope and burpees actually work?

Short answer

Yes. Short, hard sessions of 4 to 10 minutes raised heart-lung fitness as much as 50 minutes of steady cardio. But they did little or nothing for fat loss or muscle mass.

Do short workouts like jump rope and burpees actually work?
'Shorter workout → smaller payoff' — does this formula hold?
A common belief is that exercise only counts if you do at least 30 minutes. So a few minutes of jump rope or a few sets of burpees are seen as 'better than nothing'. We checked whether short workouts actually change your body.
A 10-minute workout matched a 50-minute one
After 12 weeks, heart-lung fitness rose 19% in both
People trained 3 times a week for 12 weeks, either with a 10-minute session containing just 1 minute of all-out sprints or with 50 minutes of steady cycling. Among the 25 who finished, heart-lung fitness rose 19% in both training groups. It took 1/5 of the time.
Even 4 minutes of burpees worked
Fitness like 30 minutes of running, push-ups more than doubled
22 people trained 4 times a week for 4 weeks, either running for 30 minutes or doing burpees, jumping jacks and similar moves for 20 seconds on, 10 seconds off, 8 times (4 minutes). Heart-lung fitness rose 7% with running and 8% with the 4-minute workout. The 4-minute group also did 135% more push-ups and 64% more sit-ups.
Jump rope worked too
Fitness, strength and jumping all improved
An analysis that pooled 21 jump rope studies with 1,021 people found jump rope training improved endurance, body fat, arm and leg strength, jumping and sprint speed. Muscle mass and bone did not differ.
Pooled studies said the same
Only 14 to 47% of the time, with no difference in results
An analysis of 21 studies with 849 people on short workouts (15 minutes or less per session, 5 minutes or less of hard effort) found fitness went up and blood pressure went down. Using only 14 to 47% of the time of regular cardio, the results did not differ. Going harder helped more than doing more rounds.
Fat and muscle are another story
Changes in body fat and muscle mass were small or none
An analysis of 47 studies on short, hard workouts found body fat and muscle mass did not differ from people who didn't exercise. In 11 trials with 414 people doing bouts of 5 minutes or less spread through the day, fitness rose but leg strength and body composition stayed the same.
Bottom line: short workouts are enough for heart-lung fitness
The formula breaks at the 'smaller payoff' link
When 58 people did bodyweight training for 16, 27 or 90 minutes a week for 6 weeks, the 16- and 27-minute groups did not fall behind the 90-minute group in fitness gains. 4 minutes of moves like burpees or jumping jacks, 20 seconds all-out and 10 seconds rest, 4 times a week, works. Fat and muscle need diet and strength training on top.