It's a best practice to make sure your whatever software your site is using is patched and up to the latest addition. A high risk warning from that page, "Patch SUPEE-6285 fixes a leak where hackers can take over customer's sessions and download lists of your shop's order details through the RSS feature. Released July 7th, 2015." Would certainly be worth fixing.
From an search perspective, Google has stated that security is a ranking signal: https://webmasters.googleblog.com/2014/08/https-as-ranking-signal.html
Security is a top priority for Google. We invest a lot in making sure that our services use industry-leading security, like strong HTTPS encryption by default. That means that people using Search, Gmail and Google Drive, for example, automatically have a secure connection to Google.
Beyond our own stuff, we’re also working to make the Internet safer more broadly. A big part of that is making sure that websites people access from Google are secure. For instance, we have created resources to help webmasters prevent and fix security breaches on their sites.
We want to go even further. At Google I/O a few months ago, we called for “HTTPS everywhere” on the web.
So making sure your site is secure can have multiple benefits.