Men are largely not sexually objectified in video games, I don't think. They are, quite a disproportionate amount of the time, the main agents in the game that move the story forward and take actions that affect the plot. When females are given equal time, they are not given equal significance; i.e., they don't do a whole lot besides helping the male characters.

"But Spooooon!" you might say, "FFXIII! The Strong Female Characters! SEXISM IS OVER!"

If you have played the entire series, or even a large portion of it (as I have, up to XII which I did not finish), you know that what I'm saying is true.

How does this relate to sexual objectification?

Someone cannot be being objectified and be the sole agent working to move the plot forward (by their own decisions which succeed) at the same time. Granting a character in any narrative a moment where they are successfully acting to move the plot forward all by themselves is a very weighty decision for a writer to make, and it rarely, if ever, gets given to a female character in any FF game. I would challenge someone to create an extensive list of times females were granted agency in the plotline of a FF game.

One example I can immediately pull off the top of my head is FFIV. The Magus Sisters and Barbariccia are named characters in the story who attack the heroes.

...But then, they're villains.

FFV makes out better, what with Faris being all action-y early on, but she largely becomes irrelevant in the latter half of the game, providing mostly advice.

FFVI...um. It has a Female main character, yes. But she doesn't really do anything. She isn't her own master, she doesn't make any decisions that settle any plot points. It's suggested, but never followed through on. Celes and Relm fare no better, as their actions in the story (if present) are largely ineffectual.

I could go on. Women don't really do anything in the stories of FF, unless they're bad guys.

If you are a woman, a man, or either with a daughter who plays FF, I suggest you write to SE (snail mail) and complain...

I think this is kind of a festering thing in Japan right now. They've been shouting at their female senators "Get married!," arrested an artist for making a vagina-shaped kayak or something.

Women are kind of getting shafted in that country, really.