There is no built-in feature for this in App Lab. The closest you might get is to use a 3rd party tool, as another teacher mentioned above (I haven't tried it myself), or have students copy/paste/type their code into a shared Google Doc.
From a pedagogical standpoint, some of the ideas and practices emphasized in that lesson are abstraction and collaboration. Part of the success of the project lies in breaking down a complex scene into effective chunks, which if done so can be worked on independently by multiple students simultaneously. If group members coordinated and communicated well, combining their independent parts should be a matter of copy/paste, and if their parts were abstracted well, the only additional work is defining/calling a function, say "drawScene", that calls the individual functions. To put more bluntly, if students do things "right", there's not much need for a real-time collaboration tool.