Any gate at Sea-Tac is reachable from any other gate without passing through TSA security again.
You can walk between concourses A, B, C, and D, but if you are traveling to or from the N or S gates, (you should be as they serve international flights) which are in separate buildings, then you can't walk; you must take the train. You will see signs directing you to trains which you can take between concourses. When you arrive in Sea-Tac, look for signs directing you to the N & S Gates.
If you see a TSA security checkpoint from either side, you took a wrong turn. (Though you may see US Immigration on your way out.)