Supplementary relatives allow wide range of antecedents, including clauses. (CaGEL p1035):

Pat is afraid of snakes, which doesn’t surprise me at all

The relativised element in the example given is:

Don't be trapped by dogma, which is living with the results of other people's thinking.

So he's saying that being trapped by dogma is living with the results of other people's thinking.

Supplementary relatives allow wide range of antecedents, including clauses. (CaGEL p1035):

Pat is afraid of snakes, which doesn’t surprise me at all

The antecedent of the relativised element in the example given is:

Don't be trapped by dogma, which is living with the results of other people's thinking.

So he's saying that being trapped by dogma is living with the results of other people's thinking.