It's a little awkward to translate it into English with the exact same structure but what it's saying is "We called him a 'walking computer' because there is nothing he doesn't know" (literally, "We called him, who has nothing he doesn't know, a 'walking computer'."
모르는 것 = something not known
모르는 것이 없는 그 = he who doesn't have something not known
걸어 다니는 컴퓨터:
걸어 다니다 comes from 갇다 (to walk) and 다니다 (to go/move around). 걷다 is a 'ㄷ' irregular verb, so it becomes '걸어' with the 'ㄷ' changing to a 'ㄹ'. 걸어 다니다 thus means 'to walk around' and '걸어 다니는' would be 'walking'.