Your CEO doesn’t care
A CEO who doesn't care about finance, sales and marketing is unlikely to remain a CEO for very long. This increasingly applies to technology management and disruptive innovation; the latter being a key element of digital leadership.
So one might say that technology management addresses 'run the business' activities and digital leadership covers 'grow / change the business'.
The CEO knows these things need to be done but doesn't particularly care who does them. The CIO being the tech manager and the Chief Digital Officer being the digital leader works just fine for the CEO. However he doesn't need extra headcount at the top table so the chances are that either the CDO will work for the CIO or vice versa.
CIOs who sit by and let this play out are likely to have a new boss in the foreseeable future.