You have named one of the big risks of iOS development. In general, Apple is reluctant to approve apps that compete with their own apps; they allow competing apps from major tech companies because it would be too unpopular not to, but a smaller developer is at their mercy. One of my nightmare scenarios would be to come up with a new idea, spend a year developing an iOS app, and then have Apple reject it because they were secretly working on the same thing.
Android does not have that particular risk. Competing with an app from Google might be difficult but at least the company will let you try; they have no prohibition on apps that compete with their own. Another key difference is that sideloading is possible; even if the Google Play store won't carry your app, you can offer it through other channels. Gambling apps and apps with sexually explicit content can be sold for Android though not through Google's store. Reputable third party stores will still ban the other kinds of content that Google prohibits, such as spyware, Trojan horses, and other kinds of malware.
Facebook has network effects in its favor. Basically, Facebook is popular because Facebook is popular; people want to be on the social network that their friends are on. The company also has Instagram and the Oculus Rift.
Uber has a good idea but it's not one that can be protected. They have no way to keep customers and drivers from defecting to Lyft or other services. There is no particular advantage other than habit to using Uber today just because you used Uber yesterday.
If you actually had the resources to fight that case you would have won. The Supreme Court recently reaffirmed the First Sale Doctrine, which basically says that once you buy a physical object like a book you are free to do whatever you please with it. Their license is invalid under US law and cannot be enforced.
None of that helps you in practice. The publishers are counting on the fact that few people have the resources to fight them.
"You've probably heard the warning about how "descriptions" and "accounts" of the game are prohibited without the NFL's consent."
This is a misreading of the statement. What it actually says is that use of THESE descriptions and accounts is prohibited. In other words, you can't quote their words or use their images without consent. They NFL is claiming copyright on the contents of the broadcast, which is perfectly within its rights. Exceptions would exist for journalistic use, but I'm sure that all the major newspapers and broadcasters have obtained consent in any case.
Independently talking about the game without using their words is perfectly legal. Lots of people do it. Using images that didn't come from the NFL would also be legal if there were some good way to obtain them in the first place, but because the league restricts the use of recording devices at the stadium (within their rights because it is private property) those third party game images do not exist.
You do have to be careful how you use the words "Super Bowl" because of trademark law. Using the term to talk about the game itself is fine, but using it in connection with your own non-NFL-sponsored event or promotion is not. You can't have a Super Bowl public party or a Super Bowl sale, which is why you hear so much talk of the Big Game.
There are two ways to write error-free programs; only the third one works.