There is no chrome_proxy.exe in the Dragon program folder, and Windows throws an error. If I change that to dragon.exe, instead of getting an application window (without chrome and toolbars) I get a new tab in Dragon that goes to the page, no different that using a bookmark.
Dragon version 108.0.5359.95 (64-bit)
Windows 7 Professional
Works as expected in Chrome browser, because it has a chrome_proxy.exe