First of all take care about your onsite SEO. Once your content is close to 100%, then take care about loading speed of your website since it's also a ranking factor. If your pages do not consist of at least 500+ words, keyword rich titles, content with various H tags and images with keywords in alt tags, you can try to apply that in one of the pages and scan it once again. I haven't heard about that scanner website though, so I cannot tell if the accuracy of the shown scan is good, but It would be easiest to see what kind of content is on your competitor url, then see what's missing on your url and apply what is missing. Once your onpage SEO is good and domain still doesn't move up, then it's time to make use of offsite seo, that is backlinks.
