A commemorative day established on this date because the word "word" is said as "futuba" in the Oshima region in the Kagoshima Prefecture!
The word "word" is said as "kotoba" in standard Japanese.
Either way, about the pun:
Futuba → fu(2) tu(→tou —by the way it's written—; 10) ba(8)
Don't you go talking so chummily to me!
InsideTsundere Ghost-Half-chan with a Personification♂ dialect (Kansai dialect)↑ that's the intonation (if you imitate it, you should be talking in faux Kansai dialect (maybe))The joke here is that one of the main things that do change depending on the Japanese dialect is the pitch accent, so the arrows are indicating whether you should pronounce the mora as higher or lower-pitched.
As for why the Kansai dialect in particular: the Kansai dialect is widely considered as "sounding funny" in Japan, and it's often used for comic relief characters throughout Japanese media.