So everything is as it should be. There is no reason why docker binary would not be found.
Can you check PATH
I have
Code
LibreELEC:~ # echo $PATH
/usr/bin:/usr/sbin:/storage/.kodi/addons/script.moonlight/bin:/storage/.kodi/addons/service.system.docker/bin:/storage/.kodi/addons/virtual.network-tools/bin:/storage/.kodi/addons/virtual.system-tools/bin:/storage/downloads/bin
LibreELEC:~ # docker -v
Docker version 1.13.1, build 1.13.1
and you see correct path included (/storage/.kodi/addons/service.system.docker/bin).