The plugin was designed to work with a single row of tabs. The text in your tab titles is rather long and you have a lot of tabs, so your tabs have gone to two rows.
The responsive behaviour of this plugin was designed to solve this issue at narrow browser widths. When the width of the browser is greater than the responsive breakpoint set in the stylesheet’s media query, the tabs should appear as tabs, and they should appear as an accordion when the browser is narrower than the breakpoint.
The default value of 767px for the breakpoint works well in most sites, but it needs to be a higher value for your sites so it shows as an accordion when it would otherwise go to two rows. To change the value of the breakpoint you would need to replace the default stylesheet with a custom set of styles.
The plugin documentation outlines how to replace the default styles with a custom version. You can also configure a set of styles including setting a new value for the breakpoint by using the optional Tabby Responsive Tabs Customiser add-on.