Why do we need to break down long sentences to understand them? Why do we need to break down long sentences that won't immediately scan? Is it an attention thing? Working memory, executive function?

For example:


  Studies show that if there are many stimuli present (especially if they are task-related)...".  


is a straightforward sentence. The only ambiguous term is "they". Does it mean "studies" or "stimuli"? In this case it is, obviously, stimuli, but the issue seems to be that i need to read the "they" slower, and am not primed to. What part of cognition is being tested?
First off, the difficulty in the specific example given in the question is more a matter of proper writing habits than anything else. The use of parentheses is often discouraged because it disrupts sentence structure and therefore interferes with the flow of information. Secondly, the use of referring words (pronouns) to earlier parts of the sentence are generally encouraged, barred that the pronoun is unambiguous. In the example the pronoun is ambiguous, as both 'stimuli' and 'studies' can be 'task-related'. The cited sentence is therefore a prime example of how not to write a decent English sentence and could be a textbook example for Scientific-English writing courses.

In terms of cognition, it is indeed related to working memory, as you need to remember the words in the earlier part of the sentence. Of course attention (vigilance) is needed to extract the information in the sentence. Executive function therefore is involved, as it includes all aforementioned processes.