I think you misunderstand. By default, Gecko enables just the common ligatures. But this page has the following styles:
div {
text-rendering: optimizeLegibility;
font-variant-ligatures: common-ligatures;
-webkit-font-variant-ligatures: common-ligatures;
-moz-font-feature-settings: "liga", "dlig";
-ms-font-feature-settings: "liga", "dlig";
-webkit-font-feature-settings: "liga", "dlig";
-o-font-feature-settings: "liga", "dlig";
font-feature-settings: "liga", "dlig";
}
The text-rendering style enabled optional ligatures. The font-variant-ligatures style enables the use of OpenType "liga" and "clig" ligatures, but then the font-feature-settings style overrides that with "liga" and "dlig" (discretionary ligatures). What that means depends on how your font designer flagged their various ligatures, of course, but the page is explicitly opting into more than just common ligatures.