Unfortunately, Ghanshyam, for non-natives like us, there is only one way to learn things in English. Memorize them. Especially for Indians where we have our own rules to amend the language, there is nothing we can do. Just observe native speakers and their styles and you learn. That's it.
Well, now here, it's an intransitive verb. True. That's because transitive verbs requires something to transfer! [I remember that way -transitive transfer, intransitive, no transfer, thanks grammargirl]
Said that, intransitive verbs can stand alone without any support. They won't look odd. Say--
the sentence is fine without any additional information.
is 'half'. You want 'what'? So, here, the verb 'want' is transitive which requires something to transfer. You add 'what you want' and it is a complete sentence. They call it as an object.
I want a car
In your example,
An old baggar[sic] stood (by the gate)
'by the gate' is an additional information but not necessary to complete the sentence.
Hence, they mark it with 'intransitive'.
The verb 'stand' is both transitive and intransitive but in its general (and most of?) usages, it's 'transitive'. More information is on OALD.