Well I just downloaded the Falcon 4.0 from GOG, it is a much older looking thing than what I played a few years ago. What I played is probably the version in my link to the Amazon site in my OP.
You may have downloaded Falcon 3.0 Gold. If you go to your game shelf and click on Falcon Gold’s box, you will see Falcon 4.0 under the section “Game goodies” with a file size of 367 MB. We offer the original Falcon 4.0 as an “as-is” bonus item because the game’s remaining bugs are a bit too time consuming to fix but we wanted everyone to have access to an original Falcon 4.0 executable so that you can run BMS 🙂