It seems to me like this guy almost completely writes off physical exercise of any kind. I would imagine that in another decade or so he may change his opinion as he witnesses his own physical condition begin to deteriorate. There is a pretty convincing body of evidence that indicates lack of physical exercise causes many health problems, and his solution of eating less and meditating probably won't help prevent muscle atrophy and the long list of diseases that result from lack of proper nutrition.
He seems to take an overly extreme position which appears to exclude using skillful means for cultivating more wholesome states of body and mind.
I think it important to see what he means by exercise: activity to obtain a physical state beyond what is needed to do your work, whether that be meditating in the forest or being an office worker. Specifically, he states that most people eat to support the exercise done so that the body can be enhanced, or that people eat too much, then exercise to stave off the consequence of doing so. Both of which are unhelpful, for the first, which seemed to be his focus, stems from non-acceptance that the body is a perishable item, control over which is fleeting and frustrating. The second reason was that people should be less attached to food, then they wouldn't need to do the exercise they do to avoid that.
Basically, he is advocating that we be fit enough to do our work, and that those who would follow the path further down should limit the food they eat and the physical work they do to only what is needed- as taking more than that arises from greed for form or sensual pleasure.
All this seems unsurprising for a monk to say. Kinda orthodox.
And it should be noted that monks often get fat and sick and die, and often stay thin and live long. The old school monks that lived more austere lives were thin and strong enough to live long - think of ajhan mun: he lived to 79 years old, which is not a short life. And he was mobile to the end.
Now, personally, I like to exercise. I run. I ran today. I'll likely run tomorrow. I'm thinking of taking up weight lifting. And I see a need to clean up my diet. My life doesn't conduce to quiet meditation in a cave, but to poor mental habits of various kinds. For me, exercise is a correction to my habit of sloth and overeating. Do I want to live like a monk? Maybe. I am undecided. Can I at this time? No. Do I begrudge monks for thinking like monks and prioritizing dhamma practice over my lay concerns? I'd be silly to think so.
So, to OP: if you live a wish to avoid the ego shit that goes with gym membership, then ditch the car, walk to school/work/stores/wherever (if you're going a long way, take a bus or LRT or subway or whatever), and buy only staples when you go to the grocery store. Then you'll have monk like fitness without the vanity.