I think you're overthinking this a little. While what you're considering is unusual, I can't see any reason why it wouldn't just be a written language in a logographic script.
- is purely for reading and writing
- has no need to be spoken and is thus not based upon letters/phonemes
- is not meant to be signed, hummed, whistled, grunted, tapped or transmitted in any other way except for being printed on, and read from, a two-dimensional surface
It has no need to be, sure. But if humans or human-like beings are there they would most likely develop an oral way of "reading" it eventually.
- uses symbols to represent concepts
- each symbol/concept corresponds to something like an English word or sentence (e.g. 'a cat', 'the sound made by flying bees', 'the feeling that results from being beaten by a lesser foe', 'move quickly', 'why?')
- symbols are highly domain-specific and exclusive — mining, carpentry, fishing, etc. would have exclusive symbols that only have meaning in their contexts
Sounds like a logographic writing system. Now it's not clear if the symbols for phrases are made up of component symbols for the things they represent or are unique singular symbols. Building symbols from other symbols would make sense, otherwise the number of symbols would grow exponentially.
- symbols are arranged relative to each other (in 2D space) to communicate more complex concepts and provide context
This is on the surface the biggest difference between your proposal and human languages, which for both spoken and written language are linear.
However consider that some branches of linguistics believe that all language is representable by binary trees alone. If your language has a syntax (and if it doesn't it really couldn't be considered language) then we'd expect that it would be possible to develop a tree-based representation of it, perhaps using multiple levels of deep structure below the surface. And a non-binary tree could be converted to a binary tree.
I just spent some time looking at 2D languages, both conlangs and programming languages, and all the ones I found consisted of linear paths to follow or a tree structure. Conlangger Sai has explained their ideas for a non-linear fully 2D writing system, but they don't give an example of such a writing system. But they do say that their version of non-linearity is distinguished from linear design systems only by inelegance or convolution. I'd take this to mean that actually it is serialisable (and therefore could in theory be spoken) if not by humans then by some being of great intelligence. The essay is worth reading anyway if this topic continues to interest you.
In fact, I believe I can say that it is not possible, short of crippled or very simple specialty cases, to directly convert a linear writing to a non-linear one without either loosing a lot of meaning (NLàL), being extremely inelegant by virtue of failing to take advantage of better design (LàNL), or becoming functionally incomprehensible (e.g. the list format in which an Nth-degree array is stored in the C programming language).
So, what is non-linearity?
At its core, NL has to do with how concepts are arranged, both on physical paper and in their more abstract form. A NL system is a multigraph; its components are, or can be, extremely interconnected. There is no single traversal method, though there may be some conventional ones. There may not be a ‘traversal’ method at all, as such;
