One thing to know is there is no correct way to tag a feature on OSM. 
area:highway was resurrected from an abandoned proposal, something not toughly talked though by collaborating mappers, and just one of the reasons it is not rendered by the main maps.  
This area was mapped using the
highway=footway + area=yes method which is also commonly used. Linear paths were added because path area=yes were not routable features and was requested. But if you would also want to add area:highway as an additional tag along with highway=footway + area=yes that would be ok. 