The image path is relative to file where the CSS is defined.
That file is mappress.css in the plugin directory – not styles.css – so the relative path works correctly.
I’m wondering what is different in your blog. Did you move the CSS files or definitions to your theme directory or styles.css?
If so, you’ll need to change the relative path there or make it absolute. It’s not possible to change CSS paths using PHP.
If you’re using the theme directory, files there aren’t overwritten by plugin upgrades, and if you use a child theme they also won’t be overwritten when the theme is upgraded.