As pertains to Linux desktops, a "desktop environment" is a loose term for something like Xfce, KDE, or GNOME, and typically provides things like taskbars, application launch menus, desktop icons, and to a greater or lesser extent, a suite of interoperating applications.

Which DE a user is currently running is irrelevant to the rendering of Sublime Text's sidebar. The Sublime Text process is sending commands directly to the X server. The DE is not involved.