Haha, it's just a custom theme/style, nothing more, using a patched uxtheme.dll.
Yes it's XP, I couldn't use anything higher on a daily basis and it even took me a while to get accustomed to its anal-retentiveness in certain regards after my 98SE machine got put on hold for repairs.
Anyway, those toolbars are nothing out of the ordinary for these "old" Windows versions - just right-click the taskbar and the menu offers some standard toolbars and a
New toolbar entry where one can select a folder containing links (or an Internet address).
Apparently the BaseBar class is an IE Toolbar (see
here, because
here they completely leave out the system-only window classes).
There's been a discussion on the old boards
here regarding creation of a BaseBar window but there's been no positive outcome so far. I may try my hand at creating such window too, maybe it could help with testing.
Simply naming the links in an ascending order wouldn't cut it - the bar has drag'n'drop capability within it and to/from Desktop or file managers, automatically creates links when something is dropped. Much like the QuickLaunch, which is also a target of this forced icon position flush we need.