What does the no-computers tag mean, exactly? The description reads "A puzzle designed to be solved without using calculators, online decoders or computer programming." Reading this literally, this is suggesting that the puzzle design itself discourages using a computer to solve it. However, it seems to me while reading comments and responses on puzzles using this tag that it is being used to ask that the solver is not allowed to use a computer to solve the problem. There is a meta question which actually uses this definition as a premise for their question. These sound like two different things. If it is the latter, then I wonder why we don't also have tags like "no-chessboard" for chess puzzles the OP would like to be solved in your head or "no-piano" for musical puzzles that they would prefer to be solved by humming.
In practice [no-computers] is pretty much exclusively used to mean "I, the poster of this puzzle, wish that computers not be used to solve it". This is definitely a property of the poster, not the puzzle -- and this makes it a "meta-tag", a thing Officially Discouraged on Stack Exchange sites.
And yes, [no-chessboard] and [no-piano] would be kinda ridiculous. (I take it your point is "those would be ridiculous, so why isn't [no-computers] likewise ridiculous?" rather than "let's create those other tags too".)
On the other hand:
The canonical problem with meta-tags, according to the person who coined the phrase, is that they are not suitable to serve as a question's only tag, but sometimes people will use them that way, resulting in a question that's effectively uncategorized. But that doesn't seem to happen here with [no-computers]. I just checked the most recent 100, and the highest-voted 100, puzzles with that tag: they all had other tags too.
[no-computers] differs in an important way from [no-chessboard] and [no-piano]: it's much more likely to produce an entirely different kind of solution than they are, and I think that, rather than discouraging computer use as such, is almost always what it's for. Why would I use a computer when solving a puzzle? To automate away the pain of a big pile of brute-force calculation. If I respond to a [no-computers] puzzle with an answer containing 10 pages of exhaustive case-checking, all done by hand, then I submit that I have missed the point; and if that was really the best way to solve the puzzle then it should never have been given that tag in the first place.
I take [no-computers] as a sort of abbreviation for a note in the puzzle saying something like this: "It's surely possible to solve this by brute force, but I am only interested in solutions that are simple and elegant enough to be carried out, and understood, by a smart human brain without computerized assistance." (And I take it to carry an implicit promise that there is such a solution to be found. If there isn't and the poster merely likes to make people suffer, then the correct procedure is to ignore the puzzle and move on to something less boring.)
Strictly speaking, [no-computers] is a meta-tag, and it fails a bunch of the usual tests. It can't meaningfully be the only tag on a question, it's not something you'd want to search for, it doesn't describe the content of the question. If Jeff Atwood descends from on high and tells us to nuke it, we'll nuke it. But it's serving a useful purpose, and if we nuked it we'd just have to replace every instance of [no-computers] with a note in the question along the lines I described above, and I don't see how anyone would be better off for it.