Pedantic answer:
Mobile responsiveness is not necessarily as important as mobile usability. Definition of mobile responsiveness: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwju3cXz0tbWAhWC7iYKHd8yD_wQFggvMAI&url=https%3A%2F%2Fwww.studiopress.com%2Fbeginners-guide-responsive-design%2F&usg=AOvVaw3g7qLYcSKb5epIF_QzVX9W, generally through CSS media queries.
There are other ways to ensure mobile usability that do not necessarily change the site's style/layout based on screen size and/or device. For example, making input fields/forms/menus/buttons large enough to easily be clickable on mobile can allow for a site to easily be used/accessed on mobile without (or with minimal) changes
If you look up alternatives to responsive design, you can also find information on other ways of implementing mobile usability, such as https://www.interaction-design.org/literature/article/adaptive-vs-responsive-design.