"Activate (www.activate.com) projects that in the United States eSports will have more viewers than every professional sports league but the NFL by 2021" and will need to more than double viewership to topple the NFL.
And if you consider "traditional sports" holistically like they are treating "eSports" it is more fair to consider NFL, MLB, NBA, NHL, MLS viewership together, of which have large non-overlapping segments, then the gap becomes more of a chasm.
Riot released viewership total for the Worlds finals a couple months ago, and viewership in NA was significantly down than the previous year. In fact in almost every eSport viewership figure, if you discount Chinese and Korean viewership, the rest is almost insignificant -- an MLB playoff game attracts more viewers. I will say we are in the twilight years of the NFL, but what is more likely is that another physical sport topples the NFL throne rather than an eSport.