Rolling for Horror Between Rooms with No Door
The rules clearly state that you roll a Horror Test, when a monster enters a room with an investigator or visa versa (page 15). Line of Sight has nothing to do with the question, you do not roll a Horror Test, because you can see a monster.

Room - An area of the map tile that has a name and is separated from the other rooms by solid brown walls, doors, or the edge of the map tile. ... (page 8)
Whenever a monster enters (or is placed in) an investigator’s room (or vice versa), the investigator must immediately make an attribute test called a HORROR TEST. He does so by making a Willpower test modified by the monster’s horror rating (the blue number at the top of its monster token). If he fails this test, he takes one horror (see “Damage and Horror” on page 24)