Personally I would look at the leading causes of death in (my case) the United States:
- Heart disease: 596,577
- Cancer: 576,691
- Chronic lower respiratory diseases: 142,943
- Stroke (cerebrovascular diseases): 128,932
- Accidents (unintentional injuries): 126,438
- Alzheimer's disease: 84,974
- Diabetes: 73,831
- Influenza and Pneumonia: 53,826
- Nephritis, nephrotic syndrome, and nephrosis: 45,591
- Intentional self-harm (suicide): 39,518
"General old age" isn't marked up there, and although those monkeys managed to hold on to a few more years, I don't think they're plagued by the same diseases that human beings are.
This is one of those times where I think the difference between humans and apes becomes clear. Monkeys don't work office jobs, don't drive cars, don't sit on sofas, and didn't have a more than 2x increase in their life expectancy in the last two thousand years. Medical care has allowed us to far surpass our old average life expectancy of ~30 years.
I think the more important question, and it's assumptive to think the monkey-calorie study answers it, is:
Does a reduced calorie diet mean a human being will live longer, given that the leading causes of death are completely different in humans and monkeys?
You and I have a completely different set of challenges then a monkey does, so the mechanisms we need to employ for our health are likewise very different.
For all the primary causes of death except for nephritis, exercise has been shown to seriously reduce your chances of ending up with one of them (it even addresses depression which is linked to suicide).
For Alzheimer's (2010 study):
Although extensive studies are required to understand the mechanism,
it is clear that physical exercise is beneficial in the prevention of
AD and other age-associated neurodegenerative disorders.
For heart disease (2003 study):
Although the effect of an exercise program on any single risk factor
may generally be small, the effect of continued, moderate exercise on
overall cardiovascular risk, when combined with other lifestyle
modifications (such as proper nutrition, smoking cessation,and
medication use), can be dramatic.
Strokes (2004 study):
Moreover, data from studies involving stroke and able-bodied subjects
have documented the beneficial impact of regular physical activity on
multiple cardiovascular disease risk factors and provided evidence
that such benefits are likely to translate into a reduced risk for
mortality from stroke and cardiac events.
Cancers are too numerous to make sweeping statements about, but the National Cancer Institute has demonstrable evidence of exercise playing a significant role in reducing multiple cancer risks.
Diabetes is clearly reduced by nutrition and exercise, and half of "accident deaths" are from falls, many of which in the elderly although perhaps not fatal start a chain reaction of events through broken hips and then lack of physical movement. Increasing balance and coordination reduces falls, and this has been demonstrated with fitness as well (2006 study):
Power training improves balance, particularly using a low load, high
velocity regimen, in older adults with initial lower muscle power and
slower contraction.
Summary
The study on the monkeys did not show a reduction in the primary (or even secondary) causes of death in humans. As such I think it's quite a leap to think it applies to humans in any material way as the challenges to our mortality are fundamentally different than that of a monkey.
Reducing the intake of sugar and proteins
literally means the opposite. Where did you found that point about exercises (your fantasies?) and why do you upvote the answer below which says that research addresses monkeys rather than yeast? Do you understand that apes have basically human same cells?