The reason is simple: we only have so much time in the day. Media consumption takes up a huge part of that. And while an individual's level of media consumption may rise or fall, it's relatively consistent across a large number of people.
I have a hunch the author is stumbling onto the problem of media measurement. Basically, as more forms of media are available, we tend to consume more of them at the same time. For example, in the 80s I may have watched TV while reading the newspaper. As we have added more types of media in the form of mobile, video and games, we just add more potential "double counting" (or even triple counting!) scenarios. Also, many of these usage measures tend to be self-reported; and the more dimensions you have in a self-reporting questionnaire the less accurate the results are likely to be when you add them up (rounding error, poor recall of actual times leading to "proportional" times, etc).
Media measurement is hard. We still haven't figured it out for online advertising, which should arguably be easier than other types of media since we have better mechanisms for measuring things automatically.
Things are moving towards the long tail though, so I do expect to see a continued growth in the variety of media available. But if you want to see a "zero sum" media in action, just consider that the average ratings for "Seinfeld" were 21 million viewers per episode. 20 years later, the most popular show on TV was "Sunday Night Football" with an average of only 13 million viewers. TV ratings have actually been on a steady decline since the 1950s [1]. So if you give people more options, they will watch them -- at the expense of other forms of media. That's a zero-sum market in my book.
[1]: https://en.wikipedia.org/wiki/List_of_most_watched_televisio...