Vegetables have about 100 calories per pound. (See
http://www.beyondveg.com/billings-t/cal-par/calorie-paradox1... ). You can get higher by picking the right plants so let's say 300 calories per pound. At 6,000 pounds per year that's 1.8 million calories. At 2500 calories per person per day that's enough for two people for a year.
For a family of 4 that's at least twice the area, or 0.2 acres needed, and likely more as the web page says their max was 6,000 pounds. It also doesn't say which plant those were, nor what the moisture content was. After all, if a watermelon is 15 pounds then that's 400 watermelons, and each one gets 11 sq. ft, but most of that is water weight.
And as for the gardenpool, as best as I could tell, duckweed is 6 times more productive than corn, and tilapia at best consume 1.5 lbs to produce 1 lb of weight. Not all that weight will be edible, and corn isn't as productive as potatoes, but the numbers work out that it might be 2-3 times more productive than my potato number for the same area.
However, I think the numbers for duckweed yield are in pig waste water or something else with a lot of nutrients in it, and everything is here is under best conditions, which also means a lot of care taking. Which potatoes don't need.
BTW, the web site says 8 eggs per day, not 8 fish. It looks like it takes 5 months for tilapia to mature to eating weight, and 8 fish a day would mean stocking 1,200 fish at a time. What they don't say is, is duckweed the only food source for the fish or are they adding other feed?
They also mentioned that they need a swamp cooler to keep the temperature in check. Assuming that's 200W average over 24 hours, that another 4,000 kcal ("food calories"), or almost enough for two people. They get that off the grid, but if they needed to provide their own fuel source for heating and cooling (tilapia can't handle cold water) then that's another factor in the energy equation. Potatoes are hardy in northern, cool climates.