1. Most people recognize the need to find ways to remain healthy and 2. Getting healthy helps one to cope with stress.
However, two common misconceptions I come across nearly daily in my career run throughout the article. Namely that improving one's fitness is difficult and time consuming.
Addressing the first point I'll state that improving one's fitness, whether it be losing fat or building muscle is simple, but takes effort - both to eat smart and exercise efficiently and effectively.
To quote my friend and one of the smartest people out there when it comes to fat loss, Alwyn Cosgrove, priority #1 is good nutrition. Priority #2 is see #1 - it's that important. When it comes to fat loss you MUST create a caloric deficit (using more calories then you consume) while getting enough protein, healthy fats, and micronutrients.
If #1 and #2 aren't happening then you aren't losing fat. It's that simple. Grocery shopping is key here - get lots of vegetables and lean protein sources and go easy on starchy carbs (bread, pasta, cereal). By preparing your meals at home you have complete control over portion size and ingredients.
Getting back to the NYT article the point regarding devoting time for exercise is crucial - but maybe not what you think. When it comes to changing your body composition the most efficient method is to do exercise that raises metabolism - a clue here: It isn't aerobics.
Activities that increase muscle mass and force your muscles to work hard are what will raise metabolism. Steady state cardio may burn calories, and are fine if you have plenty of time, but it won't raise your metabolism much, if at all. Strength training is, to the best of our knowledge, the best way to both promote muscle mass, stress your muscles, and best of all - it doesn't take much time.
I've trained plenty of busy people that have lost considerable amounts of fat and gained muscle training two to three hours per week. That's it. No hours of cardio on treadmills required.
However, and this is a big caveat, to get good results forget bicep curls, leg extensions, and other relics of the 1970's bodybuilding era. You need to do compound movements such as squats, pullups, deadlifts, lunges, and presses. If you can only find time to exercise a couple of hours per week than doing fullbody workouts comprised of such movements is the call.
In the space of one hour we typically spend 10 minutes working on tissue quality, mobility (keeping joints healthy), and warming up followed by 30-40 minutes of hard exercise, and some flexibility work at the end. In and out in one hour - no wasted time.
As for stress relief, it goes without saying that a good workout goes far in this regard. Make your training fun and purposeful and you will not only stick to it, but also get results.
The number one reason people stop going to the gym is no results. Number 2 is boredom. So get in the gym, outside, or wherever you like and have some fun moving your body.
I'll leave you with a bit of what I call fun (these are the guys that trained the actors from 300)