Airplay not working

[noshky]

On my RPi3 with Kodi 16.1, Airplay doesn't work neither over Wifi nor over Ethernet with my iPhone 6S, iOS 10.2.
What can we do to have this working again? I was putting quite some hope into using Airplay.

Running the suggested tests gives me:

Terminal

$ sudo netstat -anp | grep 366
tcp 0 0 0.0.0.0:36666 0.0.0.0:* LISTEN 1547/kodi.bin
tcp 0 0 0.0.0.0:36667 0.0.0.0:* LISTEN 1547/kodi.bin
netstat: /proc/net/tcp6: No such file or directory
netstat: /proc/net/udp6: No such file or directory
netstat: /proc/net/raw6: No such file or directory

Terminal

$ cat ~/.kodi/temp/kodi.log | grep airplay
19:10:03 19.886923 T:1953181696 DEBUG: SECTION:LoadDLL(libshairplay.so.0)
19:10:03 19.888994 T:1953181696 DEBUG: Loading: libshairplay.so.0
19:10:03 19.933195 T:1516319664 DEBUG: CZeroconfAvahi::doPublishService identifier: servers.airplay type: _airplay._tcp name:XBian port:36667
19:10:03 19.933334 T:1516319664 DEBUG: CZeroconfAvahi::addService() named: XBian type: _airplay._tcp port:36667