I'll make this very simple: The hot chip is warmer than the ambient air because the rate of heat transfer from the chip to the air is low. A fan will increase the rate of heat transfer, thus decreasing the temperature of the chip and increasing the temperature of the air in the backpack. It will also increase the rate of heat transfer from the backpack air to the backpack, which will increase the rate of heat transfer from the backpack to the environment.
Notably, the fan would help even if the backpack was a magic closed system (which it is not; put a 100W computer and a 1kWh battery into it, open ten hours later, and you will not have anywhere near 1kWh of heat.) But why would it help in a closed system? Because the chip does not care about the total energy in the system, the chip cares about the peak chip temperature. The chip will always be the hottest thing in the backpack, but the delta in temperature between the chip and the air can be quite large. Indeed, in practice, for "natural convection" (no fan), this dT between the chip and the air is considerable. When you add a fan ("forced convection") you shrink that dT substantially.
