The article is poorly worded -- yes, advertisers spend a lot of money, but were those advertisers to disappear, other advertisers would buy those spots. So the question becomes, to what degree does the induced demand raise the marginal profit for advertising spots. And how that in turn affects how much networks are willing to pay the NFL for licensing, and that in turn affects how much the teams get in kickbacks from the NFL. So likely marginal at best.
The flipside is also how much viewership increases because of sports gamblers watching that would otherwise not watch. Also difficult to confidently assert the value of.
Negatives aside if you are fine with the losses it could be viewed a bit like donating to the football clubs.
Larger football clubs could be fine taking pay cuts etc, but there would likely be many smaller clubs that can't pay their players on the pro or semi pro level any longer.
I am not from the US and NFL could probably handle it, but I am from a smaller country with smaller clubs. If betting companies sponsorship was banned many clubs, even in the top league, couldn't play on the pro or even the semi pro level.
They gain the most, but in addition they benefit from the sport being popular so they are willing to help invest in making sure that would be the case.