"Does not support Remote Access"

> I have enabled remote management on the router (C7000-100NAS): Https,
> port 8443

   This lets you use a web browser to access the router's management web
interface.

> But on the android genie app [...]

   That's not a web browser.

> [...] I get a "Does not support Remote Access" when I attempt to
> enable remote access on my Motorola E4.

   Is the C7000 router compatible with the "android genie app"?
Apparently not.

> Is this a limitation of the phone?

   Not if the C7000 router is not compatible with the "android genie
app".

> Or is there some other setting I need to enable on the router for this
> to work?

   No.  You need an app and a router which are compatible.  Or, you
might be able to use a web browser on the phone to access the router's
management web interface.