Well, I did some searching and it seems that neildawson is correct in that Flash Player 10 isn't compatible with 10.3. However, you might try downloading the
standalone Flash Player 9 in order to see if that might work with Panther.
You'll have to perform a couple of additional steps, too:
1. Open the folder which contains
Machinarium and Control-click on its 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. Now open Flash Player 9 and in the File menu, select Open...
5. Click on Open File... and navigate to the movie.swf file.
It's a pain, I know, but there's a good chance it will work as long as you're able to install the standalone version of Flash Player 9.
Edit: I just tested the game using the standalone version of Flash Player 8 and it worked fine, but I'd try 9 first. Of course, I'm using Tiger (10.4.11), so I have no way of knowing for certain if any of this will work for you. =o(