What can I use to recreate this older desktop-style UI?

The screenshots sound like an older Ext JS interface, possibly from the 3.x era. If you mainly want to identify the look, compare them with archived Ext JS examples. For building something new, check the current license and availability first, since older releases and newer versions may have different terms.

Could be YUI 2 as well. It had a similar early desktop-app feel, but it’s discontinued, so I wouldn’t choose it as a foundation for a new project. You could reproduce the visual details with your own CSS and use a maintained library only for the tab and modal behavior.

For just tabs and a modal, I’d avoid adopting a whole legacy framework. Plain CSS can do most of the appearance, and a small amount of JavaScript can handle the interactions. That gives you more control over matching the screenshots without inheriting an outdated component system.

jQuery UI themes or a widget library with older-looking themes may be worth a look. Check the available themes and component demos before committing, though. Similar-looking interfaces can come from several different frameworks, and a close visual match may take some custom styling.