|Billion Reasons Why, a novel|
So I wondered, how many minutes per month do people spend in their public libraries? There's a lot of data available for US public libraries from IMLS. In 2010, the most recent year for which data is available, 1.57 billion visits were made to US public libraries, or about 131 million visits per month. I have no idea how long an average library visit lasts, but let's say it's a half hour, then the total minutes of "user engagement" by US public libraries would be about 3.9 billion minutes per month. Roughly the same as Wattpad.
Maybe we should also count the time that readers sped at home with a library book, 30 minutes might be a serious underestimate. (see update) Also, Wattpad's usage is spread out internationally- they are the top mobile site in the Phillipines, for example. So its usage within the US is probably quite a bit less than public libraries. But it's also concentrated in certain demographics- teenage girls, for example. And it continues to grow at a solid pace.
Update: Karen Coyle point out in comments that you could also estimate library user engagement by looking at circulations. By that measure, assuming an average of 4 hours of reading per book, you get that US public libraries are about 8 Wattpads of engagement.
Any way you look at it, that's a lot of reading going on.