I don't think HBO is going to decimate Netflix tomorrow, if ever. But I think they're a heck of a lot more dangerous than any video game company. People aren't going to suddenly give up non-interactive media en mass, especially for a single game, cultural phenomenon or no.
There are different ways of looking at this. No matter how high a chance HBO have of doing damage to Netflix, any damage they do will be limited because Netflix are global and HBO aren't even remotely close to having that kind of status.
No matter how low the chance of a video game company doing damage to Netflix, there are video game companies that operate on Netflix-like scales that could conceivably move into Netflix's market, globally.
15 years ago the home video market consisted of video rental chains competing with each other to be the best video rental chains that they could, and maybe the market moved a few percent one way or another each year, but overall those direct competitors split the market and it stayed split, and it stayed that way for years, and then they all got killed by a threat none of them properly honoured. Having been on one side of that disruption, Netflix will have no desire to be on the other side of it.
Anything can of course happen, and CEO's should be able to react to anything—but part of business is making predictions about what is most likely to happen, and preparing accordingly. I'm having trouble imagining a scenario where 5% of Netflix subscribers cancel their subscriptions because of Fortnite, and I flat-out don't believe that such a possibility is what keeps Reed Hastings up and night, whatever he says.
It's probably good to ensure that you're aware that they're giving Fortnite as one of many examples of cross-media competition, not the only competition they face. Nobody in Netflix is talking about losing sleep because of Fortnite, they're just saying that they lose more time to a game with 125m players globally than they do to a region-bubbled streaming service with some unknown-but-smaller number of subscribers.