I think your suspicion is correct. "in need" does have a specific meaning for people in poverty."in need of" would have been more appropriate in this situation.
However, for the posting, I suppose most people can get the meaning of "in need" as "in need of the seat", althogh grammatically it could have been stated as:
"please offer your seat to anyone in need of it", or
Please offer your seat to anyone, whoever needs a seat - i.e eldery people, children, people carrying babies or young children, pregnant women or handicaps,
It also has another meaning - people who suffer poverty and hungry