Do I need a mobile pugin if my theme is responsive?

I read the FAQ and may be I am not reading it correctly….

If I have a responsive theme (I use Twenty Fourteen official WP theme), should I or should I not check off the under the Mobile device support under the Advanced tab?

I know it says “External plugin or theme required.” but in the FAQs here it reads: “Your theme is probably responsive which means it resizes the page to suit whatever device is displaying the page. If it’s not responsive, you’ll have to use a separate mobile plugin to render a page formatted for those visitors.”

That got me confuse if I supposed to check off the box that state “Mobile device support” or not.

I have added the URL of my website if anyone wants to take a look at the cached data.

Also note I do not see the following in mobile browsers source code which I do see on desktop pages. I suspect that I am not serving cache pages to mobile users:

<!-- Dynamic page generated in 2.589 seconds. -->
<!-- Cached page generated by WP-Super-Cache on 2020-07-11 18:42:34 -->
<!-- Compression = gzip -->

Thank you.

The page I need help with: [log in to see the link]