Windows XP get's the icon from shell32 for the Run dialog. ReactOS get's it from user32.
It was decided on the forum that the icon should be the cog icon (current run icon) and properly done in shell32. https://reactos.org/forum/viewtopic.php?f=2&t=14299
See http://www.glennslayden.com/code/shell32_icons.jpg and look for icon 25.