Update: I decompiled the code and found that there is no easter egg.

Here is the code for the Egg.exe program:
public void OpenEgg()
{
if (!this.GM.virusFixed)
{
this.desktopScreen.SetActive(false);
this.StartCoroutine(this.OpenErrorWait());
}
else
{
this.StartCoroutine(this.EggOpenWait());
this.desktopScreen.SetActive(false);
}
}