My photos rarely have people (faces) in them. Is there a term for such photography?
There is no term for photos that don't involve people. Photos are categorized based on what they are of, not what they are not of. A photo is not of an infinite number of things.
If I take a photo of my wife indoors, it is not of outside, it is not of cats, it is not of nighttime, it is not of waterfalls, it is not of ants, it is not of the future, it is not of a TV, it is not of stars...
Having a term for what photos are not of simply doesn't make sense.
Portraits are usually posed photographs, however if you are taking photos of people that are not posed in a traditional portrait fashion then you would refer to them as 'candid'.
You would typically call other photography types that do not involve people, something more appropriate.
From my knowledge, Portrait and Landscape are definitions of picture sizes. Usually portraits are "tall" photos" while Landscape are rotated 90º.
Its definately not about subject since you don't need people to take a portrait or a landscape photo.