If a person greets a group of people by saying Salaam Alaykum, and if someone who doesn't belong to that group hears it, does he too have to reply for that Salaam?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Whoever greets a congregation by saying As-Salaamu Alaykum, it is a communal obligation on the group to respond to his greeting and whoever hears it but is not from that group is not obliged to respond to it, because the person greeted the group and not him. However, if this person responds to the greeting, this does not exempt the group from responding. The outstanding scholar Al-Buhooti said: 'It is an individual obligation on an individual person who is greeted by Salaam to respond to the greeting if the person who started the greeting if he intended him in person, even if he is in a group, and the communal obligation on the group who were greeted will be lifted by the response for the greeting by one single person.'

Imaam An-Nawawi said: 'It is an obligation to respond to the greeting of someone by the consensus of the scholars. If the Salaam was said to one single person, then it is an individual obligation on him to respond, but if it was said to a group, then it is a communal obligation. If one of them responds, that is sufficient and the communal obligation is met. If all of them respond, then all of them have fulfilled the obligation either by responding all at once or one by one. However, if no one responds to the greeting, all of them will be sinful. If a person who is not in the congregation and who is not meant by the greeting responds, the obligation is still not lifted from the group.' This is clear evidence that the greeting did not include those outside the group; had this greeting included them, the communal obligation would have been met. It is for this reason that the person outside the group is not obliged to respond to the greeting as he was not meant. 

Allaah Knows best.