What's a word for a thing that something can be an instance of?

The word you may be looking for, immediately understandable to nonprogrammers and nonspecific enough to encompass all your examples and any others you may care to come up with, is

category, n.

....

1. Logic and metaphor. A term (meaning literally ‘predication’ or ‘assertion’) given to certain general classes of terms, things, or notions; the use being very different with different authors.

(from the OED)

The categories, in the Aristotelian sense, are the ways of describing things. Aristotle (do I need to say famously?) lists ways things may be described. His lists of such ways vary in length and in their particulars, but perhaps the most often quoted is this: things may be described in terms of

(1) substance, (2) quantity, (3) quality, (4) relation, (5) where, (6) when, (7) being-in-a-position, (8) possessing, (9) doing or (10) undergoing something or being affected by something.

(from the Internet Encyclopedia of Philosophy)

To relate this to your specific examples:

• A theatrical production (for example) is the category that includes plays, dramas, etc., that is, theatrical products. Likewise, abstraction is the category that includes an abstract.
• An economy is an element of the category economics.
• Thinking about the way you're thinking is categorical thinking.
• If a is an instance of b, then b is the category that includes a.

type -

• one having qualities of a higher category
• qualities common to a number of individuals that distinguish them as an identifiable class
• a member of an indicated class or variety of people
• a particular kind, class, or group
• something distinguishable as a variety

"What type is it?" would perhaps work. However, "What is its type?" is still plain English if the former yields an adjective rather than a noun.

If a is an instance of b then b is an abstraction of a.

The word is used in programming but it predates programming.

Abstraction

(2) the process of formulating generalized ideas or concepts by extracting common qualities from specific examples.

(3) an idea or concept formulated in this way ⇒ good and evil are abstractions

Abstract

expressing a quality apart from an object <the word poem is concrete, poetry is abstract>

A poem is an instance of poetry.

Poetry is the abstract concept that encompasses all poems.