The author says that English doesn't have an explicit way of expressing xor, but I'd disagree. I'd say that the default behaviour of "or" in English is xor. If you say "I'm going to go to the fair or the mall", you're saying you'll go to one or the other, but not both.
Expressing the || operator in english requires extra qualification, like "I'm going to go to the fair or the mall or both".