I totally agree with fun and active ONLY for three year olds. With that said, this varies by gym as well. Our gym starts the developmental path at 3 years old for kids that seem to have good focus and attention and are enjoying their classes and showing natural ability. I can't really say what they are looking for,, I would think mostly the ability to follow directions and focus as well as maybe some physical traits they may be able to see at that age, but I don't know what that would be in their cute squishy tinyness. At three my dd was immediately placed in this developmental 3 year old class.
This class is, of course, focused on fun fun fun, but it also starts the very beginnings of good form and is more focused and gymnastics directed than the obstacle course based rec classes. My dd was really frustrated, even at that age, with kids goofing off. She wanted to know how to do things right. I was happy that our gym had this option for her. Who knew where we would end up 7 years later. Oy!
This wasn't something we knew anything about walking in the door though. If your gym has a program like this then I am sure that they would approach you if you dd would be a good fit.
Their little bodies at this age need to be cared for properly and not pushed or conditioned. There natural tendencies and abilities shine through but at this stage it is about holding your hands on your hips and walking pretty and jumping and rolling around.
My one big piece of advice for the serious little ones is always keep them wanting more. The minute my dd stepped into a serious gym, she wanted to move her bed in and sleep there. All these years later that drive to want to do more has never gone away. Every year she whines that she wants more hours or to do more skills. Right where we all want her