Captivate right-click do not work in Chrome

OK.  First thing to do is update your version of Captivate 9.  You are NOT on the latest version, so your issue may simply be fixed by updating.  When you DO update, make sure you reset your Preferences before trying anything else.

Next, you need to separate the two outputs to find out whether just one or both is not working.  So DON'T use the dual publishing option but take a simple ONE slide test project with a click box set to jump to a web page on RIGHT CLICK ONLY, and then publish that test project to SWF first, then later publish separately to HTML5.

In SWF output the right click functionality is entirely dependent on JavaScript that is loaded into the related files with the SWF.  An SWF on its own will only pull up the right click menu for Flash Player.  So when testing SWF content for right click functionality you need to be launching the SWF via the HTM file that Captivate publishes and you must also have any other JS files that get published as well.

Since Flash Global Security can interfere with right click functionality when being played locally, you need to ideally test this output from a web server environment.

Let us know how it works out.

And one more thing...have you tested this output from a web server or are you just trying to play it locally?