You lose heat through radiation, but the materials surrounding you are also radiating heat. You emit thermal radiation at a black-body temperature of 37C or so

You lose heat through radiation, but the materials surrounding you are also radiating heat. You emit thermal radiation at a black-body temperature of 37C or so to the environment, but the average surface nearby (in a non-air-conditioned environment) will be radiating back at 30C or so, for very little net heat loss. The innovation described here is to replace the local environment with a chilled one that interacts only by radiation. The air with very little mass contributes negligible radiation to the system, so you radiate heat outwards but receive little in return.