I tend to do something similar (in smaller rscale) when for instance downloading a book series where each title has its own folder. Moving them to the root folder for renaming as per my standard and then dropped into the Book_Archive\Author folder.

Simply go to the root of your current archive, and initiate a search for .mobi, including subfolders. Once it's done, mark all the found files with Ctrl-a, drag and drop to (copy/move/link as per need) new directory. That should not bring along the relative paths of the files, just the file.

Might want to scan through the results before the drag ad drop, in case there might be something matching .mobi not athe end. Not sure if there's a way to tell the search in Explorer that the string must occur at the end of the filename.

Edit:
Ah, beaten by the FAQ meister because I had to go find a Win 8 machine to check behaviour hadn't changed... and *.mobi forces the match to the end/extension.