I stayed there myself and found it comfortable, too. Click to see photos and more details. Some may have some private rooms, but most are 'dormitory' in which you will have to share a room with 2-14 other people. Backpackers' hostels' here means old crowded townhouse type of building, run by several young part-time staff in turn, in which safety and comfort is not guaranteed but freedom and socializing opportunities are. I actually stayed at and interviewed the asterisk ones in addition to I.S.E.Dorm last December, so you can personally ask me more questions about them.
Private room means single, double or triple room.
Click to see more details and pictures, and make your own judgment. Gaku-so' Kyoto Seminar House Kyoto Univ.