I would NOT recommend doing STS Plyo Legs barefoot. There is a lot of jumping onto and off of the step platform at a higher elevation. You need the stability a shoe will provide. The top surface of the steps is usually textured and would be very much not comfortable in bare feet. Additionally, your feet could slip more easily and it just wouldn't be safe. While many workouts are just fine to do in barefeet (kickboxing, for example), this plyo workout is not one of them.
While we may have been born barefoot, there are very good reasons shoes were invented!