I say "targets" because all the men you end up in relationships with are billed as "straight" and Haru is an overly-energetic, horny puppy who admits he partakes in "sexual harassment" as a work pastime.
Generally you meet several characters, and will have to choose one to court.
In Japan, dating sim characters are referred to as “capturable” -- whether that means you capture their hearts or their bodies depends on the game.
While it was initially influenced by Japanese BL games, it covers more Western sensibilities. is currently available on PC only from Manga Gamer directly (though I’m told it can work on Mac via a Windows virtual machine). Korean company Cheritz has been releasing their Japanese-style dating sim games into English for a couple of years now, and recently got those games onto Steam through Greenlight.
Their latest, Nameless, is quite beautiful and differs from their last entry, Dandelion, in that it does not contain stats and instead is a straight up visual novel.
The Niflheim is probably one of the best free-to-play mobile otome game examples that I can give.