In addition to what Amy said, doing the workout also creates a balance challenge for your feet/legs, thus strengthening those muscles (i.e. foot arches, Achilles, calf, etc). Barre work is typically done barefoot or w/a very minimal shoe on, that will allow you to point/flex as needed w/proper form. If it's ok, w/your Dr, you may want to give it a shot w/o the shoes, to attempt to re-build strength in weakened areas. That is what I've been using barre wo's for, to rebuild my fallen arches that led to an Achilles injury. Maybe try it out w/o shoes, and if it seems like it's too much for you, put on shoes. You may find that as long as you don't go too deep at first, that you slowly get stronger and stronger in this area, as I did. But, if it's against doctors orders for you to do so, then by all means, you should wear shoes.
FWIW, when Cathe did this workout at the RT, everyone had on shoes. Here's a link to
the NJ RT barre class video , (you'll have to skip to about the 20 min mark for when they begin barre work).
HTH