Here we have an obvious error in 𝓟, the omission of the definite article the before camp. The original scribe here is the unknown scribe 2 of 𝓟. Oliver Cowdery, when he proofed 𝓟 against 𝓞 seems to have missed noticing that the the was lacking. Although it is possible that 𝓞 itself lacked the the, a more reasonable explanation is that scribe 2 of 𝓟 simply omitted it when he copied the text from 𝓞 into 𝓟. Note that later on in this chapter, scribe 2 once more omitted the the before camp, but this time he caught his error and virtually immediately inserted it supralinearly:
This other example strongly suggests that earlier in verse 22 scribe 2 of 𝓟 made the same copying error, although there he neglected to correct his copy.
The noun camp, whether in the singular or plural, always takes some kind of determiner or possessive premodifier in the text. If camp is followed by a prepositional phrase headed by of, the determiner is always the definite article the. In the following list, I exclude the example from Alma 2:22 where the the is missing in 𝓟; there is one earlier example of this construction in this verse and it has the the in 𝓟 (marked below with an asterisk):
In other words, the decision of the 1830 typesetter to supply the definite article the in Alma 2:22 was undoubtedly correct.
Summary: Accept in Alma 2:22 the 1830 typesetter’s obviously correct emendation, the addition of the definite article the in “the camp of the Amlicites”.