Do I get exclusive rights to use the 3D model when purchasing it on CGTrader?

Licenses

No, the designer of the product keeps the right to the product and can determine how long the product is available for sale and can sell the digital files unlimited number of times. You, as a buyer of the product, however, are allowed to use the model multiple times in your projects, with no limits imposed on the time period or sales volume of final product such as video, film, animation, video game, VR/AR application, or any project incorporating the 3D model.