You're simply reading too much into the word "magnitude." You want to translate it into technical terminology as "absolute magnitude," since the latter is often abbreviated to "magnitude" by physicists anyway.
But in everyday parlance "magnitude" is only trying to convey comparability. You have two things, each with their own magnitude, and the implication is that the magnitude of the one is equal to, greater than, or less than that of the other. This ordering property is exemplified by the real numbers. So "magnitude" → "real number" is better in certain contexts than "magnitude" → "absolute magnitude."
Your dictionary is entirely consistent (and consistent with the way I speak in the English vernacular). Note that for "magnitude" it gives
A number assigned to a quantity so that it may be compared with other quantities.
A property that can be described by a real number [...]