A good design is always the key to success. If you site is responsive it will open up nicely in all the platforms like tablet, smartphone, desktop and laptop.

It is not mandatory to have a responsive website to boost your overall rankings, however it is recommended as it will serve the following purpose:
1. There will be more time spent on your site that will boost your rankings.
2. Bounce rate will reduce, that will boost your rankings
3. Google will list it in a better way, that will boost your rankings.
4. It will be visible in proper formats from different platforms that will boost your rankings because more people will open it.
5. Search engines will fetch the links more efficiently, that will boost your rankings.

I hope that helps, for more information feel free to setup a call.