I look at my own experience. If my gardens were already set up and growing, and I only need to tend it and harvest, yes I could do that within the two hours allotted. (But not included would be my livestock, trading network, and foraging, thus it wouldn't be ALL our food.) But if I had to include prepping the garden and planting it, creating compost and mulch material plus spreading them, growing seedlings for transplanting. building trellises and container gardens, fencing the garden in from predators, preparing the harvest for storage....I don't think the two hours per day is enough time. Having only two hours a day allotted to growing a year's worth of food, I think I'd need to buy chemical fertilizers, seedlings for transplanting into the garden, compost/mulch materials, and possibly herbicides and pesticides. There wouldn't be time enough to produce my own. So if I didn't mind spending quite a bit of money, perhaps I could do it if I only counted the veggies and fruits growing on my own land.
What about storing my harvest? Did the author include that in the two hours? Could one not just harvest, but actually get stored a year's worth of food in those two hours a day? Perhaps the author had very large freezers. They didn't say. But canning and drying takes time for that much food.
Another thought? All their food for the year? Just how varied or monotonous is their diet? In my experience, the more variety I have growing in the gardens, the more time it takes. A 20' by 20' plot of potatoes is far quicker to deal with than the same sized plot planted in 30-50 different vegetables and herbs. And what about the protein aspects? Perhaps they are vegans, I don't know. But most people have eggs, milk, cheese, meat, and fish in their diet, too. Were these purchased....or included in the two hours of labor? Uuummm, things are getting complicated. Maybe the author was talking only about the vegetable part of their annual food supply. Just what is included in the definition of "our year's worth of food"? Is the author buying herbs and spices? Fruits? I'm curious what veggies are included, but the author didn't say.
The article was promoting the idea that if a person simply worked at it two hours a day, they could have all their food for the year. Personally I think there's a little more to it. The person would have to be willing to eat a limited diet restricted to what would grow in their region. Plus they would have to have the experience and knowledge to pull it off. Plus luck that some disease, pest, or quirk of nature didn't wipe out their garden.
My objection to these sort of articles is that they target the novice gardener who is already at a disadvantage with lack of experience, knowledge, a fully functioning garden. They can easily be set up for failure. Setting a two hour per day target is an awfully high goal to achieve, and in my opinion is an unrealistic goal. I'd be hard pressed to do it myself. I could easily see a novice gardener becoming thoroughly discouraged when they couldn't produce all their own food on that time schedule. Personally I don't like to see articles that set people up for failure. I'd rather see ones that encourage people to try without setting such lofty goals.
ps- Still mulling this over, the author lives in an area with snowy winters. This means that they can not grow food for several months during the winter. Thus they have less days available than me to get in their 2 hours of food production. I can grow food year around. Even so, I don't think I'd be able to produce all our own food in just two hours a day. My livestock takes at least a hour a day, leaving only an hour a day to the fruits and veggies (not including trading and foraging).