Godot’s MIT license certainly let’s you redistribute the engine as part of your proprietary game. However, it equally lets others redistribute their games under the same open source license, or even a copyleft license. So it’s spirit seems equally business, hobbyists or free software moralist.
Copyleft helps me by making sure my code can’t be included in a proprietary software. My code is there to be copied but if you make changes and redistrubte them then I get access to those changes. Maybe I use them in my software, thus improving it.
Do you indend to share the code and files for your game? If not then put it where you like. If you plan to share the code then I’d be tempted to keep the license for that code in a folder with it, and move that readme to it.