Was there a flight to IXJ on any other carrier after your original flight left DEL?
If so, you could have insisted that they put you on that flight, regardless of the carrier.
If not, then you could have insisted that they put you in a hotel overnight and then pay for the first flight next day.

Jet might argue that when offered an option of a flight to ATQ and then travel onward by taxi, you voluntarily chose that option and they don't owe you anything else after that.