What is a .git.dmp file and how can I use it?

Check if it is possibly a git bundle. If that's the case, you can simply clone it to a new directory:

git clone whatever.git.dmp whatever

This blog post has a good explanation of using Git and Unfuddle. In short, it says to:

mkdir reponame
cd reponame
git init
git fast-import < ../my-unfuddle-backup.git.dmp
git checkout master