Gov 99 is meant to help you write the thesis in three main ways: 1) by providing deadlines to keep you on track and get your writing; 2) by focusing on peer-review of your work; 3) and by building a small and supportive community of individuals who are in the same boat as you are.
The Department takes Gov 99 seriously, which is why only faculty members and the most experienced TF are selected to teach this course. In general, you should think of it as playing a supporting role to the advice and mentoring you get from your primary adviser. A good way of thinking about this is that your primary adviser is helping you with the content of the project, and Gov 99 is (hopefully) helping you with more prosaic details (e.g., discussing how best to organize chapters, explaining what role a literature review plays, talking about how to effectively present data or cite sources, and so on).
Note that the successful completion of Gov 99 in the Fall term is a requisite to continuing to write a thesis. Meanwhile, Gov 99 in the Spring term culminates in the physical submission of the thesis to the Department (but is completely independent from the grading of the thesis itself).