I mean there is a male character you can save in the dungeon since the first game. Not just her.
This is not true. Rolan7 had it exactly. Most of the time you are a dude and there are totally helpless female damsels (who also work as pseudo prostitutes in 'kissing parlors' where they are treated as property.) that do nothing but stand around waiting to be rescued and who go crazy and start running around in a panic if they are disturbed in anyway and if you rescue one you get a kiss, which gives you a heart. (Although really, in most cases I would sacrifice them instead, they are by far and away the easiest way to get favor points, and I would rather have the reward for sacrificing two damsels worth of things then two extra hearts.)
After doing a fairly luck based challenge you unlock the dressing room where you can go into and switch into a damsel as your playable character with the hero acting as the new damsel which is simply a skin swap. Amusingly your run cycle is still a hysterical panic run.
There is another guy, who you can meet after beating a 'world', Danial the miner or short cut dude or something I think his name was. But you certainly don't rescue him. You can pay him a huge sum of money to make shortcuts to the start of worlds. But he is perfectly fine without you. Once you unlock all the shortcuts you can play as him.
This is of course in the first game. Which as I understand does not actually have any bearing on the video. But still. It might be fair to say the first one was sexist. Although likely parody sexiest. Which I am sure everyone has there own thoughts on.