"Unless your website is already an authority in your niche, your website should pass as many of the mobile requirements as possible. Older, existing authority websites seem to work fine. Whereas Google has been known to "re design" the old, outdated website to a friendlier mobile version on the spot. Whereas newer websites without traffic, trust and authority, will see their pages having a difficult time ranking for any keywords with search volume.”
Doing a quick Google search for "Is your web page mobile friendly?" will bring up a free mobile testing tool where Google will analyze your website and provide suggestions for improvement.