The interest in the monsoon can sometimes be obsessive

Yes perfectly correct. The underlined part namely ‘these’, a demontrative pronoun. is essentially an adjective that modifies its following noun rains. Please note the verb is a plural ‘rule’. Hence, the noun or any pronoun that stands for the the pronoun must be plural. Monsoon cannot be its antecedent, because monsoon is singular. At best you can call it as these monsoon rains, when the noun monsoon itself acts as another adjective, while the plural noun rains still remains the referent for the pronoun these

I assume that you wonder whether these rains (plural) should agree with the monsoon (singular). That's actually something of a contentious issue. Some usage experts say that when demonstratives--this, that, these, those--are used as adjectives they need only agree with the nouns they precede. According to that view, the sentence is fine. Other experts say that the demonstrative adjective+noun must agree in number with the earlier noun to which it refers. According to this view, the sentence is wrong because these rains is plural, while the monsoon is singular.

Which rule does the GMAT follow? As far as I know, the GMAT avoids the issue altogether.

You can find OG SC questions that test the use of demonstratives as pronouns, rather than as adjectives. In these questions the demonstratives are not followed immediately by nouns, and must agree with their antecedents, just as all pronouns must.

Here's an example from the GMAT Prep test:

Salt deposits and moisture threaten to destroy the Mohenjo-Daro excavation in Pakistan, the site of an ancient civilization that flourished at the same time as the civilizations in the Nile delta and the river valleys of Tigris and Euphrates.

a. that flourished at the same time as the civilizations
b. that had flourished at the same time as had the civilizations
c. that flourished at the same time those had
d. flourishing at the same time as those did
e. flourishing at the same time as those were

Here, C, D, and E are all wrong partly because they use the plural those to refer to the singular civilizations.

By the way, remember that even conscientiously written and edited books, magazines, etc. may not use the same version of Standard Written English as does the GMAT.