Quite apart from this vague impression I have that the Japanese celebrate
turning another year older on New Years rather than on what we'd call a
birthday, (which is, I think, why Ranma 1/2 had Valentine's Day stories,
and New Year's Day stories, and Christmas stories, and fall ghost festival
stories but never a birthday story),
I think this is more of an artifact of the fact that time doesn't seem to
pass in the Ranmaverse. If it did, all of the main characters would be
25-26 years old by the time the manga ended.
But looking to other series, we do see birthdays being celebrated on the
actual birth date. I remember several birthday stories in KOR, for example.
As for the story itself, it's yet another 'Ranma gets fed up and buggers
off' story. Bleah.