No, your AP test satisfies the area A requirement. The writing requirement refers to the Special Subject Area Requirements in this
page. The requirement applies to BS degree as well even though it is listed under the BA degree section. (They don't want to list the same thing twice.)
"1. Writing Requirement.
At least six designated General Education courses that meet the following criteria: (1) the courses require one to three papers totaling at least 1,800 words, exclusive of elements like footnotes, equations, tables of contents, or references; (2) the required papers are independent of or in addition to written examinations; and (3) the paper(s) are a significant consideration in the assessment of student performance in the course. Students may, by petition, request that up to two other UCSB courses be considered as applicable toward this requirement. Special instructions for such petitions are available from the college office. Once a student has matriculated at UCSB, the writing requirement may be met only with designated UCSB courses. A list of courses that meet the writing requirement may be found on page 115."