fought in the second World War
fought in the Vietnam War
fought in the World War II
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
It is similar to the following example:
performed in the film
performed in the "Ted".
That one should not have the "the":
performed in "Ted".
"Second World War" is not it's name, it is more describing what it was - "the second war that involved the world", in the same way that "film" is not it's name, it is describing what it is. The name is "World War II" and "Ted"
The Vietnam war:
Vietnam War has a second name - Second Indochina War. Both of these use "the ". However, if it was called the "Indochina War II", it wouldn't use "the".
Second Word War is the Proper way in American English to write World War II using Ordinal Numbers. Roman Numerals on the other hand do not have an ordinal equivalent. See Vaibhav Garg's answer in this question.