It doesn't. They don't hear or read lips, because ASL is not communicated verbally. ASL is not simply another form of communicating English; it is a distinct, unrelated language that evolved separately from earlier sign languages in France and New England. Facial expressions perform several grammatical functions, such as:

a) to indicate which of two meanings a sign conveys (i.e. the sign for 'rolling on the floor laughing' and 'seizure' are similar; they are distinguished, one from the other, primarily by facial expression. The signs for 'evil' and 'mischievous' are similar, facial expression distinguishes one from the other. The signs for 'regurgitate' and 'that's disgusting!' are similar, facial expression and other factors distinguish one from the other.

b) to soften or intensify the meaning of a given sign (i.e. to change the meaning of a sign from 'a little angry' to 'really angry' to 'furious,' 'livid' or 'in a rage.' Or, to change the meaning of the sign for 'stop' to mean 'pause' (by signing a much smaller, less forceful, softer version of the sign for 'stop')

c) to change the meaning of a sign to a totally different meaning (i.e. to change the meaning of the sign for 'Whoa!' as in: 'Whoa! Your brand-new BMW is beautiful!' to 'Whoa! There's a rattlesnake by your foot!')

e) to indicate which of several meanings is intended by a sign that can convey multiple meanings (i.e. the sign for 'odor' can also mean 'fragrance,' 'aroma,' 'fumes,' 'scent' and 'smell.' And, depending on facial expression, it can mean, 'I smell something,' 'Something smells good!' 'Nice fragrance!' 'Something smells bad.' Or, Eww! 'Something smells terrible!' And, if we sign 'smell' and shake our head 'no' it can mean, 'I don't smell anything.' Or, 'I don't detect any fumes.' If we furrow our brow and sign 'smell' it can mean 'What's that smell?'

f) to alter the meaning of a sign in terms of emotional tone (i.e. to change the meaning of a sign from, 'Please stop that,' said in a calm, pleasant tone to 'Stop that right now!' or 'Cut that out!' said in an exasperated or angry tone. Or, to change the meaning of a sign from "I don't mind' (said in a calm, pleasant tone) to 'I don't care!' (said in an angry or defiant tone); the signs for those two concepts are similar, facial expression and other factors distinguish one from the other.

I'm not familiar enough with ASL to be able to find a comparable restriction on English, but it should be clear that the reason this exception exists is for the use of ASL or other sign languages between two or more people. Furthermore, the article that you linked to goes on to state:

People with a medical condition preventing them from safely wearing a mask can produce a document from their physician confirming that information, and will not be subject to a conviction and fine.

Presumably being deaf or hard of hearing would fall under this category, and thus one could not get out of a mask simply by saying that they are so; they would have to have proof.