I just got this on my LaunchBox a few days ago and also noticed that it doesn't have a fullscreen option other than Alt+Enter.
You can make a script that sends those keys right after launch though, I did that and it works like a charm. this is the script I use:
Set WshShell = WScript.CreateObject("WScript.Shell")
obj = WshShell.Run("""cotton_reboot.exe""", 3, False)
WScript.sleep 3000
WshShell.AppActivate ("Cotton Reboot! ver1.00") 'Focuses game window just in case
WScript.sleep 200
WshShell.SendKeys "%{ENTER}" 'Sends ALT+ENTER to enter in fulscreen mode (720p)
Paste the above code into a text editor, save as cotton_reboot.vbs, put it next to the game's exe, then make LaunchBox launch that vbs file instead of the game's exe (or Steam URL).