Can an avel play dreidel during Chanukah for money?
An avel shiva should not play dreidel, because he should not come frivolous behavior during the shiva) unless he is doing it in order to preserve a specific minhag). However an avel during shloshim and the rest of the year would be permitted to play dreidel during Chanukah, as it is not considered like being metayel.
Note; The poskim strongly discourage playing cards etc. for money. .
Y:D 391-1,Aruch Hashulchan ibid 2, M:B 671 D:H Vnohagim, Aruch Hashulchan 670-9.