Action Engines are singletons and class clusters are an instance scoped variable, not global. So. If you want an exact equivalent then you have to jump through hoops like using a queue or a FGV (just like an AE-DOH!). The migration means you get new VI methods for each ENUM entry (I've talked before about code bloat) and forcing the user to drop a load of different VIs from a palette or quickdrop. You don't get a lot else apart from increased complexity and the ability to wave the "I'm using OOP" banner.
Personally. I would prefer a polymorphic VI over a class because you still have the code bloat but don't burden the user..It looks like you have just swapped the enum for a drop-down menu and you get the adapt to type for the different inputs.
If you want it as a class because.......reasons. Just wrap the action engine in some class methods (one for each enum). That's pretty much what you will end up doing if you don't use a queue and you can still wave the banner
However. if you promise and "cross your heart and hope to die" that you will only have one instance then a normal class (with a DVR?) will suffice .