The styles still apply regardless of what menu they are used with. To make your SiteMenu use the TreeView control, use the following SiteMenu control in your layout.master. You will have to remove the current SiteMenu Control for this work.
<portal:SiteMenu id="SiteMenu1" runat="server" UseTreeView="true" HideMenuOnSiteMap="false" TopLevelOnly="false" IncludeCornerRounders="false" />
You will also need to copy styletreeview.css from the styleshout-coolwater skin to your skin. Once you get the TreeView working, you will have to adjust the CSS to make it look like the jQuery menu you are referencing.