Sneaking peaks at the women's breasts/crotch/etc, giving them gifts to try to convince them to have sex, and the hilariously awful pornographic sound effects going through the whole. It's entirely possible in this case it'll turn out to be a brilliant satire of the all the terrible porny shit in games, or it could turn out to just be gross porny shit. We wont know until the game's out.
As to why it's potentially problematic, well, treating women as "goals" to be achieved without any agency of their own is problematic especially since it's so incredibly widespread in games. Also, as ridiculous as it sounds there are actually a lot of men who, to varying degrees, actually think giving a woman attention or gifts entitles them to sex and get anywhere from sulky to outright violent when their advances are rebuffed. Obviously a game isn't going to turn anyone into a predator but this kind of thing (as well as TV and movies, of course) does help to normalize this kind of behavior and is part of the reason sexual assault isn't taken as seriously as it should be in pretty much every single culture in the world.
The other issue I have is that I am sick to death of the fact that the majority of games that feature any female characters feel the need to include porny shit whether its absurd proportions, sexualized costumes, naughty camera angles, or actual porny writing or mechanics. I'm fine with porn, I really am. Sometimes I even enjoy it. I'm even fine with there being porny games but it would be really nice if I could play games with female representation that DON'T have a bunch of porny stuff more than once in a blue moon. This isn't really a problem specifically with Killer Is Deadas a standalone game, but it's a problem with Killer Is Dead in the greater context of video games.
If the world wasn't full of creeps and I could actually think of the last game I played with decent female representation that wasn't sexualized then I wouldn't have any problem with Gigolo mode, but that's unfortunately not the world we live in and it's not the world games like Killer Is Dead exist in.