Contrary to popular belief, video games aren't just for killing an idl

Clauses are "dependent" or "independent" only based on the presence of a main subject and main verb. Here we have "games aren't," a subject and a verb, neither one subordinated by a relative pronoun, preposition, or subordinating conjunction, so they are a Main Subject and a Main Verb. Later, we have "variety ... has begun," another subject and verb, again Main Subject & Verb because they are not subordinated. Two independent clauses require either a semicolon or a coordinating conjunction (FANBOYS).

Furthermore, the verb cannot be "have" in the second clause; the subject is "variety." Remember, anything following a preposition, such as "of," is NEVER the main subject of anything. "recent studies" is the object of "of," not the subject of "have begun."

In terms of pronouns, pronoun ambiguity only has to do with whether or not there is one clear logical antecedent, agreeing in number with the pronoun. An ambiguous pronoun does not make a sentence "dependent." Take, for example, the following paragraph:

"I am really happy with my GMAT tutor. He is professional and knowledgeable and on time and knows a lot about the test. I am thankful for this, because it is a difficult test."

All three sentences are clearly complete sentences and fully independent clauses. "He" in the second sentence refers to "tutor," and "it" in the third refers to "test." Obviously on the GMAT this never happens, since Sentence Correction only tests single sentences. However, the moral of the story is that, in English grammar, pronouns do not have to have their antecedents in the same sentence or clause.