its bromance and very interesting . ıt gave me the similar feeling , with ghosts
http://www.mangago.me/read-manga/yuurei_apato_kanrinin/
But this type of story has more shounen ai than yaoi tho.
Closest match is ayakari-zoushi. It is as vague as natsume lol. Got the same slice of life atmosphere with youkais but with a little more bl hint
Other bl youkai-human interaction stories are
Shounen-ai
Mauri to ryuu,
Koori no mamono no monogatari,
Daydream nightmare
Yaoi
Yami ni tooboe(and basically all aono bohra's fantasy works)
Hakuyou ayakashi gatari
For anyone who has watched or read Natsume Yuujinchou, are there any yaoi manga that have the same atmosphere or plot and/or similar characters?