What does the `shell:` prefix do in the Run dialog?

The dialog accepts commands, file paths, or URLs (URIs). The shell: prefix acts as a URL scheme, much like http: or ftp: or mailto:.

'Shell' is a traditional term for the OS component that handles the overall user interface (taskbars, program launching, file management) – in this case, Windows Explorer is the graphical "shell". The "Run" dialog is also part of Explorer.

So "shell:" addresses are URLs recognized by Windows Explorer itself to open various miscellaneous locations (similar to how web browsers might have "about:" or "chrome:").

It seems that the list of accepted "shell:" URLs is based on this registry key, specifically, the Name values of each of its subkeys:

HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FolderDescriptions

For example, shell:my video will look up the registry key where Name = My Video, which nowadays points to the ~\Videos\ directory.