The Prisoner (Condemned Man) and Soldier are friends, brought together through a long period of solitude in the penal colony together. The Traveler, however, has no real connection to either of them, and acts as a sort of objective viewpoint on the colony and its inhabitants.
Because the punishment machine acts as judgement, and is a sort of allegory for accepted religious doctrine, the Traveler does not accept it as gospel and rejects its use. When he leaves, with the Soldier and Prisoner chasing him, he does not allow them to follow him:
...the Traveller was already in the boat, and the sailor at once cast off from shore. They could still have jumped into the boat, but the Traveller picked up a heavy knotted rope from the boat bottom, threatened them with it, and thus prevented them from jumping in.
(Kafka, "In the Penal Colony," records.viu.ca)
The Traveler, representing the abandonment of religious fervor, leaves the colony alone; the Prisoner and Soldier, though they have had their faith shaken, are still representative of the penal colony and so could act as missionaries. According to this interpretation, the Traveler was likely refusing them access to the outside world so that they could not continue spreading the dangerous beliefs from the penal colony. Alternatively, he did not want to be responsible for their actions, as one is a criminal and the other a friend of a criminal.