I think the title of this thread is a little misleading. It seems to me that the author of the NY Times article was not trying to argue that chefs are as tough as elite athletes or have the same level of conditioning or fitness. The basis for the comparison is that they are both physically demanding professions that can only be worked at for a limited number of years before wear and tear on the body takes its toll. As Annabelle and Celeste pointed out, this is true for any number of manual labor professions. A good buddy of mine is an arborist on the cusp of 50. His Dr. just told him that he'll need to stop working pronto because of the nerve damage in his hands and arms.
I think there are a number of things about restaurant work though that do make its physical challenges different than other manual labor jobs. I grew up in the restaurant business and cooked professionally for close to 20 years before switching careers. Physical issues were definitely factors that spurred my career change. The hours are the first thing that springs to mind. 10-12 hour shifts (frequently more) were the norm in the kitchens I worked in. 60+ hour weeks are common in the industry. Working 6 days a week, or many days in a row without a day off are also common. I have many friends in the building trades and the vast majority of them work 40 hour weeks. The only time any of these guys work 6 days a week is if they choose to pick up a side job on the weekend. None of them have ever worked 10, 12, 14 days in a row without a day off.
You are generally also spending the entirety of your kitchen shift on your feet, often on a hard tile or concrete floor: not all kitchens provide mats for employees to stand on. Unlike my contractor buddies, kitchen workers generally do not get to sit and take a 1/2 hour lunch break mid shift. Ditto morning and afternoon breaks. Additionally, and this is especially true for line cooks, all of this standing is done in one place. You might need to go to the walk-in or dry storage, but generally you're stuck at your station with little chance to move around other than bending to reach into a low boy and twisting between the range and the pass.
Lifting heavy things is also a daily part of the job. The comparison between cooks and bakers was made upthread. Yes, flour comes in 50lb bags, but so do potatoes, onions, carrots, turnips, cabbages, etc. Meat comes in 80lb cases. I worked my way through college and my first year of graduate school in a high volume barbecue restaurant. Thursday, Friday, and Saturday mornings I'd prep 3 cases of pork butt, 4 cases of ribs, 4 cases of brisket and 100 chickens. That's nearly 1,000 lbs of meat that I'd move (by myself) from the walk-in to the kitchen and finally into the pits. The frenetic pace of restaurant work also causes cooks to try to minimize trips, so carrying big loads is the norm. I can't count how many times I have seen line cooks pile a sheet tray with full 1/6 pans of mise en place and hustle it into the walk-in.
Along with the heavy lifting comes constant fine-motor repetitive motions. Celeste made the point that kitchen implements aren't heavy. That's true, but while a pair of tongs may only weigh 6 oz. or so, squeezing them 100s of times a day every day for years on end is a perfect recipe for repetitive motion injuries. Same thing with knife work, or shaping bread and pastry. These tasks may not require brute force, but the constant repetition of specific movements can cause serious and painful injury. I suffered bilateral carpal tunnel syndrome that thankfully improved once I stopped cooking professionally.
To answer your questions Mitch, yes I absolutely agree with the author's premise that cooks have a finite number of years in which they will be physically able to do the job. As I mentioned above, I cooked professionally for a hair under 20 years. To heck with the golden years, it was the thought of not being able to get out of bed in my late 40s that motivated me to get out of the kitchen!