They exist as a concept. A concept is stored in the brain. Or on paper. Or someplace. It doesn’t have an existence of its own removed from some form of host that can either store it or use it.
To me, space is physical is a proper label. it’s not empty.
If it is a conceptual space – let’s ‘get abstract’ here. Consider this:
Who is conceptualizing? A human? How does a human conceptualize a space? Typically utilizing the cognitive processes of the visual system that simplifies outlining of objects and a space concept is imaged in the mind’s eye as a “room” – either with walls, or without walls.
There’s a limit to the resolution, but we have pan and zoom capabilities and an emotion (also physical) of “woah” that makes us feel “as if” it’s intangible. But it’s tangible, once you know what hooks to hang your conceptual coats on.