Hi. I'm not sure this is true for all games, but for some, even when Windows volume is turned down and you can't hear anything while playing the game, FBX will still record sounds, on Windows 10 at least. You'd best give it a try with your game though.

Can you upload it to a free file sharing site like Dropbox or Google Drive and then send us the download link? We can't help if we don't have a clear idea of what the weird sound is.