Is there a specific term I could use in a floor plan for the doorway leading from one room to another? For example: a person is in the living room and looks through the "doorway" that leads into the kitchen. Obviously there is no door, but is this opening still referred to as a doorway?
Doorway would indeed be acceptable. Consider that, if the doorway has a door, you cannot see through to the other side unless the door is open. In this case, depending on your angle and the location of the door, it is perfectly possible that the door is entirely invisible. If so, its existence or non-existence is irrelevant to your perception of the doorway (or frame). So doorway is applicable regardless of the existence of a door.
You might consider entryway and entranceway.
A passage for affording entrance.
Word Origin: (1740-1750); Americanism; entry + way
Peeking his head through the entryway, he saw a tiny figure hunched over a lathe in the dark interior of the room. The Temple of thé Wild Geese
This is an odd type of room—no windows at all—and no door in the entranceway—There must be a door. How did I get in here? Tumbleweeds: An Authentic Collection of Windblown Tales of Americana Caught in the Cross Hair
There's no door in the entryway to the structure, and you suddenly understand that one is not necessary. What Lies Beneath the Clock Tower
The technical term for this is:
An interior doorway or opening with all the trim and molding installed, but without a door or closure.
For an entrance between two rooms without the door trimmings, I would therefore suggest simply "opening".
- A doorway, entrance, or gate, especially one that is large and imposing.
In the UK, estate agents' descriptions of property distinguish between a "doorway" (i.e. what the OP describes) and a "door". For example "Entrance Hall ... doorways to various rooms, door to:- Guest Cloakroom ..." (quote from http://www.rightmove.co.uk/property-for-sale/property-17919543.html) The photos in the link show that one of the "doorways" between two rooms has no door.
In a properly drawn floor plan it should obvious whether or not there is a door in a particular location, without any verbal description.
I think that calling it a doorway is valid, for many of the good reasons that others have pointed out, however, it does also have to do with exactly what information you may or may not be trying to convey.
For instance, if you were describing an apartment to a prospective renter, they might be interested to know whether or not there are doors on the doorway; calling it a doorway does leave open the possibility that there might be doors. If you wanted to emphasize that there are no doors, then calling it an archway, or some other term, might be more precise.
If it has all the trim and molding of a doorway, just there is no door, then you'd call that a cased opening: http://www.dictionaryofconstruction.com/definition/cased-opening.html
But as others have said, we'd be getting too technical here. Doorway would still be understood and accepted everywhere but in the most snobbish or English circles.