As this issue still persists in 2022 I thought I'd confirm that the workaround from @dandepeched still works (MX Keys, 2022) - Thanks a lot!
I only needed to remap the play/pause button. The prev/next buttons worked as expected.
Before remapping the key combination in Options, the play/pause key on the keyboard would control media playback in the browser regardless of what program was in focus.