Interesting! You seem take "language" really far / different.
How about something like editing an image in Photoshop? There's a vocabulary (the commands) they get applied to the image. There are also rules (constraints). One could argue using photoshop is communicating with a computer, what to do with an image.
So while I say language is a misnomer for PL, you say it's a misnomer for natural languages. ;-)
I guess you could argue for it. Command resize can only be applied after something is selected, and not deselected in the meantime. You might be able to describe the Picture Manipulation Commands language using a finite automaton, and if not, using a grammar.
My views on this are highly shaped by my university lessons on formal languages [1], which I also taught a bit teeny bit. You would have text in mind, but the mathematical concepts are actually more generic than this. One of the exercises was modeling a PIN electronic door lock with a finite state machine (how to unlock without unlocking too early?).
These formalisms look like computer science stuff but are actually directly taken from Chomsky's work [2], a (bio)linguist who was/is actually concerned with human languages (which another commenter implicitly mentioned [3])
I guess this stuff is probably valuable to study natural languages, given the correct scope, since it was made for it (xD). It sure is useful in computer science in any case.
One direct result of his work is the (in)famous stack overflow "You can't parse HTML with a regex" post [4] (since regexes can only define regular languages, and HTML is not a regular language - although I believe the answer is a bit wrong, you can find a regex to parse the regular subset asked in the question, though you need to watch for cdata sections (in XHTML) and script and style tags (in HTML), at which point maybe just use a proper HTML parser unless you are dealing with well known content with no such exceptions)
How about something like editing an image in Photoshop? There's a vocabulary (the commands) they get applied to the image. There are also rules (constraints). One could argue using photoshop is communicating with a computer, what to do with an image.
So while I say language is a misnomer for PL, you say it's a misnomer for natural languages. ;-)