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The only thing is that your screenshot is cropped when you fill the form and show us the error. Let's start anew.
a. Clone the original form http://www.jotform.com/help/27-How-to-clone-an-existing-form-from-your-account.
b. Make that matrix required again and send us the link here so we can check it thoroughly in your account, not our clone version of your form.
I look forward to your reply.
I suggest you just continue responding on the original thread http://www.jotform.com/answers/556092
I checked your jotform http://www.jotformpro.com/form/51090581428959 and I found that the matrix field you mentioned was NOT set as a *Required field on the form.
Please try updating the matrix field using its property and set the *Required option to 'Require an answer on every cell'
Follow the screenshot below
Again, please respond on the original thread here http://www.jotform.com/answers/556092
I also have copied my answer to that thread.