I don't know the meaning of "salt allowance"
You cited the second meaning of the word allowance in your dictionary, but the example you quoted might have been best understood in conjunction with the first meaning:
- an amount of money that is given to somebody regularly or for a particular purpose
- an allowance of $20 a day
- a clothing/living/travel allowance
- Do you get an allowance for clothing?
In this case, the Roman soldiers were periodically given a certain amount of valuable salt as a substitute for cash wages. (This much-cited piece of etymological historical trivia is disputed, though.)
One of the more common uses of the word in the US, by the way, is for the pocket money that parents give to their children, which may be intended to cover necessities like school lunches or clothing, or may be purely discretionary, or more often a mix.
For example: When I was in 7th grade I got an allowance of 26 cents a day, which covered a six cent carton of milk at school and left me 20 cents to spend as I saw fit. (This was a long time ago, and even back then was a pretty skimpy allowance relative to some of my peers, though of course some of my classmates had parents who couldn't afford to give them any allowance at all.)
For that reason referring to a adult's budget as an "allowance" can have derogatory overtones, especially when referring to money given by a spouse who works for cash wages to one who does not. Be careful when using this word.
Since you are asking about a definition given in the Oxford Learner’s Dictionaries, you may be interested in the English Language Learners Stack Exchange site.
In this case, the book you were reading was likely pointing out an interesting fact: That Roman soldiers were literally provided rations of salt, which was termed salarium, and eventually that word broadened to refer to a soldier's entire wage.
This same history provides the basis of the expression worth one's salt, often negated as not worth his salt meaning, in a literal sense, not worth the wage one earns.