One other thing that occurred to me: maybe that version of Flash Player isn't working correctly on macOS Sierra. Perhaps you could download the standalone Flash Player and run the game through that. (Will edit in a moment here where to find the standalone Player, etc.)
Edit #1: The link to download the latest version of the Flash Player projector: https://fpdownload.macromedia.com/pub/flashplayer/updaters/24/flashplayer_24_sa.dmg
Edit #2: You'll need to open the Machinarium.app from the Flash Player projector.
Edit #3: To do that, you'll need to perform a couple of additional steps:
1. Open the folder which contains Machinarium and control-click on the Machinarium application.
2. Select Show Package Contents and then open Contents/Resources.
3. Locate the movie.swf file and move (or copy it) so that it sits right alongside the application for Machinarium.
4. Control-click on the movie.swf file and choose Open With, and from the list find the version of Flash Player that you just downloaded.
Edit #4: It's a temporary solution...until you hear back from Amanita, but it's possible it could work in the meantime.