Interesting. So Article VI (3) reads: "3. Companies of either Party shall not be subject within the territories of the other Party, to the payment of taxes upon income not attributable to sources within such territories, or upon transactions or capital not attributable to the operations and investments thereof within such territories." But Article VI (1) reads, in part: "1. Nationals and companies of either Party shall not be subject to the payment of taxes, fees or charges within the territories of the other Party, or to requirements with respect to the levy and collection thereof, more burdensome than those borne by nationals of all third countries."
So as an individual, this treaty does not help. You should read the Thai-US treaty on double taxation. You can probably get a credit on your US taxes for income taxes paid to Thailand.