One other thing that occurred to me: Machinarium has its own built-in version of Flash Player, and it’s possible that version of Flash Player isn't working correctly on macOS Sierra. Perhaps you could download the standalone Flash Player projector and run the game through that. (Will edit in a moment here where to find the standalone Player, etc.)
Edit #1: To download the latest version of the Flash Player projector, go here:
http://www.adobe.com/support/flashplayer/downloads.htmlAnd then look under where it says
Macintosh and click on the link that reads "Download the Flash Player projector".
Edit #2: You'll need to open the Machinarium.app using 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.