(Parenthetically, I recently saw that R’ Elyashiv was asked why saying this tefilah is not a problem of saying a tefilas bakasha on Shabbos, which we try to avoid. The GR”A even went so far as to omit the Harachaman… parts of bentching. The answer is that a bakasha of ruchniyus is not a problem, but I am not sure I understood the point correctly, so don’t trust me on that.)
R’ Ya’akov Shapira, R”Y of Merkaz haRav, said (link) that his father used to give tzedaka and daven for cholim just before the time of hadlakas neiros based on this Hagahos Maimoni. Even though the hadlakah is usually done by women, the chiyuv of hadlakah applies to men as well (if there is no women at home, a man needs to light for himself). Since men share in the kiyum mitzvah, it is a zman of tefilah for them as well.