I don't entirely agree with their description.
From my point of view and in the Cisco world, autonomous access points are AP's that are 100% independent. Meaning they require nothing but power and an Ethernet cable for data, to be able to do whatever they need to do. No controller (local or cloud), all configs are done locally and individually, which is why they suck for enterprise, who wants to SSH into 50 access points? no way jose.
Meraki access points are like a Cisco access point that are in lightweight mode, meaning it needs to be able to talk to a controller (cloud) just like the Cisco lightweight AP needs to be able to talk to the WLC (local) to get its configuration, settings etc.
Local mode lightweight access points require the WLC 100% to function, so if the WLC is down, the AP is down.
Due to that fact, I would say that Meraki access points operate more like HREAP/FlexConnect access points in the fact that they only send control plane data to the controller (cloud or WLC) and data plane is local traffic. If the controller goes down, its not a big deal, the AP still functions. This is how Meraki access points work too, although bear in mind there are some caveats to this situation just like with Cisco access points (see link below):
https://documentation.meraki.com/zGeneral_Administration/Cross-Platform_Content/Behavior_during_Conn...If your a Cisco person and your writing that statement, I could see why they would think Meraki is like autonomous, they do not require a 'Cisco controller' to function. However it could probably use more clarification that they are not actually 100% autonomous, they still require a controller that lives on the Internet to get initial configs.