This issue was solved on discord.
Here's what the error was in the full log file.
Running command: [/Applications/Stencyl-full/plaf/haxe/haxelib, run, openfl, -verbose, build, -debug, project.xml, flash]
[haxelib] sh: neko: command not found
Process 'haxelib' exited with code: 127
In the end, the issue was that neko had been installed on the computer, but Stencyl didn't have permission to access the /usr/local/bin folder. The solution was to run this command in the terminal (with an admin account).
sudo chmod 755 /usr/local/bin