tl;dr 169.254.x.x addresses should only appear on a misconfigured network as a fallback mechanism to retain IP connectivity. This isn’t Plex’s fault, it’s just trying to use a valid interface on the host machine. My advice is to fix your network.
With that in mind…
An IPv6 stack will always bring up link local address, regardless of whether you’ve DHCPv6, SLAAC or a staticly configured address on the interface, it’s always there for communications you don’t want/need to pass outside your local network segment.
IPv4 only configures itself with a link local address if the interface is configured for DHCP and doesn’t successfully get a lease assigned. A router will not tell a network station to use a 169.254/16 address. Link local addresses are always configured by the DHCP client (be it on a client device or an interface on the router configured for DHCP) as a fallback in the event of DHCP lease assignment failure.
It sounds to me like you’ve got an interface (or sub interface) on your Mac that’s not disabled, believes it is connected to media (be it a copper or radio PHY), is configured to obtain an IPv4 address using DHCP, but for some reason isn’t. The most likely reason is that there’s no DHCP server servicing requests on that network segment.
You say the interface with the 169.254/16 address isn’t shown in the network pane. Try the following from the terminal and see if there’s an interface with the offending address on it:
ifconfig | grep -C 5 169.254
The interface must exist for you to be able to ping the Airport 169.254/16 interface.
You say:
The 169.254/16 block is a RFC, the mac is doing the absolute right thing in setting up the route, the airport utility is doing the absolute right thing in setting it up. The equipment between here and there doesn’t always conform to the RFC though since its an edge case.
Further, even though I can actually ping my airport router from my mac on the 169.254/16 address, plex gets into trouble because it macOS doesn’t let it use that address because it’s just a placeholder for admins to go in and fix stuff.
Are you using this link local network between your Mac and Airport by design?
It’s interesting that you say your Airport also has a 169.254/16 address. As a router, it’s best practice to staticly configure the IP addresses on its interface(s). Is there a DHCP server on this network segment? Most people with an Airport use it as the DHCP for their network.