This would show only the files involved in the Pull Request in JSON format.
Former userAccount Deleted
It would be nice to have a separate URI on the pullrequests resource to get the files in a pull request. The only work-around currently is to use the /patch URI and grep the text output to look for the lines beginning with diff and pick the file from the end of each such lines. It would be nice to have a separate URI or have additional qualifiers in the /patch URI to return the files preferably in JSON format.
I've created a ticket in our internal tracker for this feature request. Watch this public issue for updates on this feature.
Issue #7639 was marked as a duplicate of this issue.
If you generate the /patch data using hg diff, you could come close to a list of changed files using hg diff --stat.
I have written a script that uses this unreleased api, and it parses the /diff output to generate a list of files. It doesn't list deleted files though, only files that exist after the diff is applied.