Safari won't play Amazon Prime Video on my iMac?

You might want to check your Silverlight plugin and confirm that it's installed and working properly. According to their website titled: Prime Video System Requirements for Computers, these are the versions supported:

• Mac OS 10.7 or newer
• Safari (version 10 or newer on Mac OS 10.12.1 or newer)
• The minimum supported version of Silverlight is 5.1

If you have the correct versions then make sure that the Silverlight plugin is enabled and configured properly in Safari, as shown below.

NOTE: You can navigate to HDD → Library → Internet Plug-ins to verify that Silverlight is installed.

Safari 12 and Amazon Prime

Curiously if I merely navigate to Prime Videos I'm able to play videos without any additional plugins using their built-in HTML5 player.

Additional research turned up this other AD Q&A titled: Silverlight Plug-In in Safari 12 which indicated that Silverlight was no longer supported in Safari 12.

References

• Amazon Prime Video & Safari: Let's Call a Truce