The airlock is the latest addition to the boarding process, when linking two ships close enough crew members will be able to travel between the two ships and board other ships to help for repairs, help ships in distress invaded by unknown bugs for example or other events. Since each crew have individual traits some may not be suited for some of the missions, lets say a crew member doesn't like weapons so sending that crew member to a mission to board a pirate ship may be very hard for that crew member to survive a fight inside with any weapon, most probably he or she may become a hostage so it will be up to the player to decide what to do with the hostage situation.
What no transporters? from technology point of view, transporters are just an easy solution but in this universe there isn't any, so people use airlocks and space suits to travel between ships or use space transporter tubes that can help people travel between ships.
Here is a concept screen showing two ships linked with a transport tunnel so crew members will float in the middle and travel slowly in 0g. You are the captain of the ship and you can give orders to crew members but they may not obey you blindly all the time, especially when scared or in distress.