Eri says they were supposed to give a kiss using the wild boar, and Yakumo says that, indeed, she is doing it so. The pun is that in Japanese wild boar and author have use the same kanji (猪), but have different reading.
Actually, author is not written using 猪 at all. There is no pun; the joke is that Yakumo has the little boar in her mouth, so its snout touches Harima between her lips.
Completely out of character for Yakumo, by the way...
