Very likely Delhi underground and bus has their specific app for it, that allows travellers to touch their phones at the turnstiles instead of NFC cards. Indeed it's very possible, but it's down to the particular underground/subway or bus authorities to allow it and to make it happen. Like Transport for London would have a custom TFL fare payment app issued that allows people to use their phones instead of Oyster NFC cards.
There are apps to read the NFC fare payment cards with your phone, maybe to get a balance, or add credit, but that's not what you were after of course.