The solutions to the clues are
Network latency (+6) = PING Support (+14) = BACK Rocky hill (-4) = TOR Parasite (+6) = TICK Monster in Japanese folklore (+10) = ONI Email folder label (-10) = SENT Sad or feathers (+16) = DOWN Unit of music (+4) = BAR Water source or street name (+7) = MAIN Pelvic joint (+6) = HIP Quiz (-11) = TEST Long sentence (+8) = LIFE
In each case, the number of blanks is double the length of the clue answer. For each word, we can "double" it and shift one of the letters in the second half by the given amount to create a word that fits in the blanks. The resulting words are
PINGPONG BACKPACK TORPOR TICKTOCK ONIONS SENTIENT DOWNTOWN BARBER MAINTAIN HIPHOP TESTIEST LIFELINE
The shifted letters spell out OPPOSITE TO IN, which is OUT. We can perform the same process with the final (+1) to arrive at the answer OUTPUT.