Hello, I know you have received some responses here already but I feel like there were some wrong thoughts provided here.
I have been helping startups and Small/Medium companies grow their traffic through inbound marketing. At my small hybrid marketing agency, we stay up to date on Google SEO requirements (Google releases a document every so often with changes) <-- we follow this document.

One of the previous answers mentions that you don't need to be mobile friendly. This is wrong, you do need to be mobile friendly and more so you need to design a website with the mobile first approach. If you want to achieve first-page ranking for a particular phrase by paying someone to give you a ton of thin/fake backlinks then you might not need a mobile friendly website but the results won't last. Probably won't last more than a month.
Now you must consider that is not about having a 'responsive' website more so than it is about the code you use to build it, the tags you use, and the information you provide to sites like Google to let them know you have an optimized mobile experience including being responsive.

With that said, nowadays is almost ludicrous to have a website that isn't mobile-friendly at a minimum because it will hurt your conversion rates. So even if is not for SEO purposes, you do need to have a mobile friendly website.