I've never used Haxe, but I would assume that it's just spitting out regular Source Maps (maps source variables/lines to compiled), which are interpreted by all major browsers. To learn more about it, I suggest this article: html5rocks.com/en/tutorials/developertools/sourcemaps
I'm currently playing around with Haxe to create a simple little web framework. Everything but the front-end framework (Yahoo Pure) is being written from scratch using a combination of Haxe/HTML/CSS. I'm writing it in FlashDevelop, using USBWebServer, and a couple of custom build/deploy scripts to copy the output JS to the UsbWebserver host directory, and to launch Google Chrome and point it at http://localhost/myserver/whatever.
Yet somehow, by some black magic, the Google Chrome developer tools (opened with F12) have a "Sources" tab which
Correctly points to my Haxe source files in the write directory
Displays the sources with simple syntax highlighting
Allows me to add breakpoints in the haxe code itself
AND lets me see the value of variables (included objects) by highlighting them with my mouse when a breakpoint is reached (like you'd see in Visual Studio or other fancy IDEs)
So how the hell can Google Chrome do this? My "launch script" is just this:
"C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" "http://localhost:8080/mysite"
This all seems like (extremely useful) black magic.