Games where the player character is female and potential objects of affection are male are known as Gx B or otome games.
Homosexual relationships are also possible, as there are games with no specific gender lines ("all pairings").
There are also GL games, which focus on female/female relationships, and BL Games, which focus on male/male pairings.
There are many variations on this theme: high-school romances are the most common, but a dating sim may also take place in a fantasy setting and involve such challenges as defending one's girl from monsters.
This time, Kei and his friends are now second year High School students.
The class has two new transfer students and they are both cute monster girls!
One game series that often includes dating, with the goal of marriage, is the farming sim series Harvest Moon.