Rusty,
for just one HotPot activity, it is probably easier to recreate it from scratch on the Moodle 2.7 site.
If you want to backup on 1.9 and restore to 2.7 you will need to make sure you back up the course files on the 1.9 site. Since you can't back up selective files form the course files, you will need to include ALL the files from the course containing the HotPot activity you want to transfer.
When you restore on the Moodle 2.7, you can select which activity you wish to restore.
But first of all, I suggest you ask the instructor to recreate the HotPot on the Moodle 2.7. It is probably quicker and certainly more empowering from him/her to do that.
regards
Gordon