Yes, that's right. International students take the same test as Americans. And it is an absolute requirement.
Graduate admissions committees, however, will be more lenient to a foreigner, as far as the score on the Verbal Section is concerned (remember, they will know your scores in each of the individual sections; not just the total). In fact, I think they will only use it as a criterion for elimination rather than for comparison. If you have a moderate verbal score, they will not preferentially select another candidate because of a better verbal score. But if you do have a very poor verbal score (which I don't believe you will - I'm just speaking hypothetically), they might eliminate you on that basis.
Most American universities also require a spoken English test : the TSE and TOEFL are the most common. Many universities will require this score as part of the application package, but very few will allow you to take the TSE after admission.
Here's my advice for your GRE. If you can, spend the rest of your time preparing for the verbal part of the test. The math and analytical sections are too easy. If you are good at memorizing, I recommend you go through all the words in a (Barron's or other GRE guide's) vocabulary list. This is probably the best thing you can do in the short term to help your score.
I believe most universities graduate application deadlines are coming up this month or the next, or are you planning to apply for 2006 ? Anyway, best of luck for your GRE !
If you have any further questions, feel free to PM me. As an international student, I went though this whole process a few years ago.