The textbook gives a historical manumission formula with aw. Its wording does not apply the stated effect to both named persons at once; an individual still needs to be identified.
«هذا حر أو هذا»
This one is free, or this one is free.
The text treats this like «أحدهما حر», “one of the two is free,” and grants the speaker wilayat al-bayan, the authority to specify the intended person. The principle concerns an effect attached to one unspecified alternative.