Firstly, 'दिल्ली एक गाँव नहीं है' is not wrong.
Hindi uses the indefinite article एक much more sparingly than English.The absence of an article can either indicate definiteness or indefiniteness in most situations. It is never wrong to include it but it is required only in a handful of situations like when introducing a brand new subject into the conversation.
For example, when you are talking to someone who is completely unfamiliar with Delhi, 'Delhi is a city. It is in India", you would use 'दिल्ली एक शहर है। वह भारत में है।'. However, when you want to say 'Delhi is a city. It is not a village' presumably to someone who's at least somewhat familiar with Delhi, you'd say 'दिल्ली शहर है। वह गाँव नहीं है।'.