Unfortunately, your understanding is not quite correct. To understand the reason for the commas properly, you should know the difference between defining and descriptive qualifying phrases/clauses[1].
Defining qualifying phrases/clauses" are necessary for the understanding of the sentence.
Defining qualifying phrases/clauses are not off-set by commas.
Descriptive qualifying phrases/clauses" are not necessary for the understanding of the sentence.
Descriptive qualifying phrases/clauses are off-set by commas.
The subject is "reaction".
("This" is a determiner and demonstrative adjective. It is required as all singular countable nouns must have a determiner.
Drastic is an attributive adjective and defining - there are many types of reaction - and this tells you exactly which category "reaction" falls into.)
"and thoroughly illegal" is descriptive and not defining. Note that "and" is a conjunction, and thus creates a new clause/phrase.
The commas signify parenthesis - it is as if the part of the sentence between the commas were in brackets:
"The most drastic (and thoroughly illegal), reaction has been the emergence of Sci-Hub..."
Descriptives can be removed and the sentence will still be correct and understandable.
Descriptives are optional information - something that the speaker adds as an aside, i.e. descriptives are extra information that the speaker thinks that you might like to know but which are not truly important.
Imagine I ask you to identify a thief from among 10 suspects and there is only one man wearing a hat...
Compare
The man who is wearing a hat is the thief. Here, who is wearing a hat is definitive and necessary because without that, we do not know which man you are indicating. You will note that there are no commas.
The man who is wearing a hat*, and who lives near to my brother's house,* is the thief. Here , and lives near to my brother's house, is descriptive because that information is irrelevant to me - it might be interesting, but it is not necessary.
[1]there are other names for these qualifiers e.g. defining and non-defining are also used.