What I observe is campus cafe is a direct object, it receives the action, went is an action verb so it should be transitive. But here: http://www.chompchomp.com/terms/intransitiveverb.htm it says it is intransitive. Can someone explain what is my mistake?
The error is that "Campus cafe" is not the direct object of the verb "went." "Campus cafe" is the object of the preposition "to". You might want to read Chompchomp's article about direct objects.
They (Chompchomp) are right that "went" is intransitive. That means we don't say, "James went the cafe." If you want to say where James went, you can use "to" (a preposition): "James went to the cafe."