The basics is, as mentioned above, there is no spring.
In the Akins, there is a spring. Once you pull on the trigger area, the gun goes to town without any mechanical interaction from the user. This, by definition is a machinegun.
However, the slide-fire doesn't have a spring. The trigger is fired consecutively by the forward push by your other hand. You can pull and hold the trigger all day long but the gun will only fire once, until you push the gun back forward so your finger can activate the trigger again.
The ATF's stance has become more and more clear over the years. As long as there is an element of human interaction (moving something) involved, then it would be considered pulling the trigger. It doesn't matter if the gun causes you to pull it really fast.
Look at the trigger activators, hand-cranks etc. All of those are legal because there is human interaction. With the Akins, once you depress the trigger, the human interaction stops, you just hold your finger in place and the gun does the rest.