Hey, so, I don't know why it wouldn't detect the buttons before entering the config menu, never heard about this until now, I'll put it on the list but at this point it pretty unlikely I'll be able to do anything about it.
Not sure what's going on with the "aim straight down" button either, I'll put it on the list.
Regarding controller button names not matching, this issue has been around forever and I *think* there's still a message on the config screen telling you about this.
This issue is not very easy to solve since all controllers use different button IDs for each button, so lets take this imaginary example:
PS4 X Button ID = 0
Xbox A Button ID = 1
Off Brand PS4 Controller X Button ID = 2
Off Brand Xbox Controller A Button ID = 3
As you can see, this poses a big problem if Button ID 0 = X/A Button in the engine, it would now give you a completely different button name for Xbox A Button since it's ID is 1, same for the Off Brand controllers.
And this is why the buttons do not always match (or rather possibly never match) since there is no way for me to know what button I'm dealing with if they all use different IDs.
But as long as the buttons actually work as you bound them then this is somewhat fine, not ideal of course but at least you can play with the bindings you want.
And with all that being said, I'm working on an update to the demo which will be using a newer version of the engine and as such this may or may not be working better now, I can't be sure until it has been tested though, so we'll have to see if this is still around when the updated demo is out.
But yeah, glad to hear it worked better on another PC and thanks for telling me about these issues, as mentioned I'll be putting some of them on the list and try to fix them later. :)