I want a different program to execute my game with a command line that contains various parameters such as the level number. Is that possible with a Unity exe?
It is possible to run unity with some predefined command lines for more info look at this page. if u are passing ur custom command lines like level u should be able to read them through the following function,
System.Environment.GetCommandLineArgs()
but i doubt if it will help u!!.. What are u planning to do exatly?! if u want to start the game with the level progress (like saving game data and loading on startup), you can use a loading screen that loads the saved level number from last time using Playerprefs class. If it is for testing purpose have a menu in the loading screen(simple gui buttons) to skip to the level u want!!
Anyway i think it was helpful
Edit: I know it is old, but sorry! this cannot be done for custom arguments!