Sorry, my bad.
I forgot to mention that you need move the images to the right position if you compile in Lazarus.

That's what the following lines in the main.pas are for:
[pascal]
// Path to data
const
{$IFDEF DARWIN}
// Keep the original path to /Contents/Resources in the .app - file
PATH = '../Resources/';
{$ELSE}
PATH = 'DemoRes\';
{$ENDIF}
[/pascal]


The Mac OS applications are basically just a folder. Right-click on the application and click on "Show content" to show the contents of the application.
/Contents/Frameworks is where the frameworks should be stored if frameworks are needed
/Contents/MacOS is where the executable is
/Contents/Resources is where resources like icons, images, sounds should be stored

When you compile with Lazarus, you can see that Lazarus creates such an application.
You need to copy the Arial16.phxfnt and the tx09.png to /Contents/Resources of the application.
The compiled application should now find all files.