Hi RMerlin,
From reading their (Akamai) paper, I think they need that the Router (e.g. a vulnerable ASUS router) has already at least a UPnP service active (potentially several). So imagine, one has launched an application on your computer on the LAN (e.g. a video conferencing tool or game for which the exploit could work, it seems that not all UPnp opened port can be exploited), that application has opened a port on the router using UPnP.
Then the attacker just need to scan the router WAN interface, it will detect the opened port, and it seems it can then craft a SSDP probe toward this port or send a specially craft HTTP URL using the `Location: ` header. If the UPnP port is "vulnerable", it can then be exploited to open other UPnP port from the remote WAN interface.
For the attack to work, you need a vulnerable router where UPnP is activated. Then you also need to have an application on your LAN requiring UPnP and which is currently running (so has probably opened the port), and that port needs to be exploitable (it is not clear from the article which are vulnerable but potentially UDP opened port cannot be exploited using crafted HTTP, or TCP opened port cannot be used for SSDP probes, etc.) and they are I guess other factors which could prevent the exploitation. I agree that my description is still vague but the current document is not particularly clear on how this can be exploited (for good reasons in a way).
But anyway, while waiting for Asus to provide a patch, better disable UPnP (if you know how to configure Port Forwarding, and application can have a fixed port defined, then usually you can avoid UPnP all together).