Hypertext theory appears to be represented by three separate undertakings.
Personally, I represent the latter.
(Very few people are conversant across all three domains, though it is probably common to have people who are familiar with two.)
And there is the recent rise of the hypertext theorist, someone who might not know anything about programming but who is able to bring a critical theory tradition to think about what sort of thing hypertext is, or might be.
The people who design hypertext software and attempt to implement various visions of what hypertext is are hypertext programmers. These people represent (from my point of view) the technical side of hypertext theory, and deal with the theoretical pragmatics of implementing various visions of what a hypertext system is.
There are what might be described as hypertext information managers (I would include a lot of HTML users in this category), people who use hypertext systems to catalogue, publish, distribute or otherwise organise information.