I don't think that's a local server address, that looks more like Adobe's Live Preview address.
In the latest versions of DW, the old Preview in Browser has been a little buried and replaced with "Live Preview" when you hit F12. That new functionality uses Adobe's servers to show you your page, live, as you make edits, or at least it's supposed to. It's notoriously buggy.
You can still get to the old Preview in Browser (its name has changed to Open in Browser) by either right clicking the file name in the Files window, or if your documents are set as tabs, by right clicking the named tab for a given document and choosing "Open in Browser".
If you prefer Open in Browser, there is a way to modify the program to re-map the F12 key to the older preview style, it's relatively easy, but does require modifying a program file.