I don't want to discourage a "high-school kid", but don't believe everything you read at its face value. In this case, the author is comparing apples and bananas and thinks the answer is oranges. An ordinary bloke can sustain an output of ~100 W of mechanical energy over several hours (a trained athlete for endurance events, a lot more). A medium car engine can typically sustain an output of 150,000 - 200,000 W of mechanical energy, even though its engine is notoriously inefficient (~25 -35%). The most efficient mechanical energy producer is the electric motor, some types exceeding 95% efficiency.
Now I'll tell you why the human body is not efficient. First of all, a lot of energy is used inflating and deflating the lungs, even with zero mechanical energy output. Even more is used pumping blood and lymph round the body. Then there is the electrochemical energy used up by the brain. Not to mention the conversion of chemical energy used, just to heat the body up to an efficient working temperature of 37°C or thereabouts, to allow the liver and kidneys to function and so on. All this requires about 1,500 kcals/day, before you blink an eyelid or raise a little finger.
Unfortunately, there is a lot of confusion between calories and kilocalories. The latter used to be written Calories, just to add the confusion. The calorie is the energy required to heat 1 gram of water at 15°C through 1°C. This is equivalent to 0.0012 Wh or 4.187 joules. The kcal, which is the unit designated for dietary intake, is 1,000 times greater. So, when your article states the guy is burning "515 calories/hour", this is not true, he is burning 515,000 calories/hour. Makes quite a difference, doesn't it.
Have you thought why you feel hot when you make a physical effort? It is precisely because muscles are so inefficient. When you eat, a lot of energy-intensive chemical reactions take place. One of these laces your blood with glucose, which is the chemical fuel for your muscles. When you use your muscles, this glucose is "burnt" with the oxygen, an exothermic reaction, producing lactic acid as the "ash". This has to be transported away from the muscle as fast as it is produced, otherwise the muscle fatigues or cramps. The lactic acid is broken down by the liver, requiring more energy. This exothermy causes a tendency for the body temperature to rise, compensated by the dissipation of latent energy by the evaporation of sweat.
Alexander Pope wrote in 1711:
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There shallow draughts intoxicate the brain,
And drinking largely sobers us again.
I'm afraid the article you quote is, indeed, a very shallow draught.
Your other point is harnessing kinetic energy. I'm not even sure you understand fully what it is. Roughly speaking, it can be called momentum. When a cyclist freewheels down a steep hill, he accelerates, gaining kinetic energy, free, gratis, energy supplied by Mr Newton's gravity. At the bottom of the hill, he continues and he doesn't have to start pedalling until he is half-way up the next hill, because of the acquired kinetic energy taking him up (he doesn't reach the top because of friction of the bike mechanics, between the tyre and the road surface and with the air). So as much kinetic energy as possible is reused. Where this kinetic energy is wasted is when the brakes are applied, when it is converted to heat at the brake block surface. In hybrid cars, mechanical brakes are used only rarely, most of the kinetic energy during braking being converted to electricity to charge the battery. So, yes, with intermittent motion, kinetic energy can be usefully recovered, provided the machine is designed to do so (most cars aren't).
Hope this makes things clearer.