In the sentence: I thought that they were game traits.
what type of clause is that they were game traits
I thought that they were game traits.
The underlined clause is called a 'content clause'.
It functions as complement of the verb "think". Content clauses are the default kind of finite clause, and serve to express the content of the words they complement, hence their name.
Note that you will also see such clauses (wrongly) called 'noun clauses' in some grammars. Modern grammar does not use that term since it is thoroughly misleading.