When sending a text message to multiple recipients, how does one see the other recipients? I sent a text message through MightyText to 5 recipients. One of them showed me on his phone it indicates the other people the message was sent to. How is this possible? Does SMS include each recipient in each message?
This is called group messaging. In short, everyone in the group gets replies from all the other group members. You can choose to remove people from the message or isolate specific people to message separately, and for that reason it will list all "participants" in the message. 

I am not sure how to view them in your app as I have not used it, but in most messaging apps, when you are in the message thread, there will be an option to view group participants. It may be hidden behind the menu key (3 dots often in upper or lower right, or hardware menu key, if your phone has one). Or it may have its own button. (Tip: in many apps you can find out the purpose of a button by pressing and holding the button)