I think it's less about having a terminal emulator and more about having access to the shell environment. In the case of acme no terminal emulator is used but you still retain access to the system tools you are given and typically access through a shell.
In the tag bar, type Win and middle click. You'll get a terminal.
You can definitely see why in the video, starting from 15:25. I don't use terminal emulators, but for other editors and from my experience, it's the keybindings and the text processing on the shell output. Acme took that to an extreme.