Annotation: I. I. Rabi, on the discovery of the muon.

When you order something from a catalog, you are, in effect, commanding that something occur (that your goods be shipped, e.g.). Hence your (1) and (2) are not essentially different.

Contrast: "First e, then one, then pi. Who ordered [i.e., imposed the apparent order] that, your secretary?"

This is offered in the hope that it may induce you to entertain the possibility that your horizons may be less all-encompassing than you seem to suppose.

No. The URL you cite gives my example as meaning 1, arrange; and both of yours as meaning 2, command, of which a-d are variations.

The word "ambiguous" is not meant to be negative here.
It only points out that the sentence can have more than one meaning and can be used in different situations.

誰がそれを命令したか。
Who ordered that? (Gave the command?)
誰がそれを注文したか。
Who ordered that? (Who ordered something from a menu, etc.)

Order something to be done.
vs.
Order a thing.

Your comment is not responsive. If you say the sentence can have two meanings, then--by the authority you cite--those should be (1) arrange and (2) command, not your (2a) and (2d).

Annotation:
This sentence can have the following meanings.
1. Who issued the order to do that?
2. Who ordered that thing (from a catalog, etc.)?
3. Who arranged the order of that (list, etc.)?

A definite improvement; however, the ambiguity inherent in the English seems--in your annotation--to be biased (at least) by its Japanese reflections: you put (2a) and (2d) [variations on "command," rendered differently in Japanese] on a par with (1) [arrange], and neglect (2b) and (2c) entirely.

All in all, it might be best to leave the tag, suppress the annotation, and contribute the Japanese sentences that illustrate your thesis.

On the other hand, this exchange of comments, if preserved, provides--with no further changes--a fulsome background.