The diagram below displays the pairs of three-letter words. If you read the four letters around each four-vertex that have not yet been used, starting with the circled letter, and then order these tetragrams in the only way that makes sense, you get the message:
NOWR EADA ROUN DSIX THVE RTEX
Reading in a circle around the sixth four-vertex (i.e., the one you
found RTEX around) is the answer JAYHAWKS.
Archivist's note: This puzzle had also had a trained answer, as described in the training page. The flavor text mentions the boss having weird friends, so we apply the answer from Jack, SWITCH THE ANSWERS, to get the new answer SECOND PERSON PLURAL.