Ah, that makes sense @Zombeaver, per the LaunchBox controller support.
Per the controller code being different between LaunchBox and Big Box, both LaunchBox and Big Box use the exact same code, pulled from the exact same library. So there's literally nothing different. It's not even duplicated code, so there's zero chance anything *could* be different. The only thing I can figure is that something else in Big Box is interfering with the Steam Link's ability to use the controller. It's pretty odd.
One thing to note is that LaunchBox uses traditional Windows Forms as the Windows technology behind it, while Big Box uses WPF (Windows Presentation Foundation), which is a more modern technology than Windows Forms, but it's still been around for quite a few years, since Vista came out. So that could be it, but why the Steam Link wouldn't support WPF is beyond me.
My only guess is that there are window focus issues when running Big Box over the Steam Link. Neither LaunchBox or Big Box will take game controller input when the window isn't focused, for obvious important reasons (otherwise Big Box would be doing things while you're playing games). Since Windows Forms and WPF are slightly different technologies, that could be it...maybe, idk.