Short answer:
You are going wrong in assuming that the calorie intake accounts for all of the radiation of the human body. A human body really emits a power of roughly $1\ \mathrm {kW}$.
Long answer: As you've shown, any black body near room temperature with a surface of $\sim 2 \ \mathrm {m^2}$ emits in the ballpark of $1 \ \mathrm {kW}$. This means any object with that surface area and whose emissivity is near 1, emits such a power at room temperature (so even a dead body!). The extra $100\ \mathrm W$ due to calorie intake a human can make use of is usually mostly used in heating, because body temperature is usually at a higher temperature than room temperature. Nevertheless, if the room temperature is at a higher than 37°C (human body temperature), then this extra 100W due to calorie intake will be used to keep the body temperature near 37°C, for example by sweating.
In short, the extra calorie intake usually translate in emitting $\sim 1 \ \mathrm {kW}$ + $100 \ \mathrm W$. Thus we see that the calorie intake only accounts for about 10% of the total power radiated. That's what you were missing.