Even the stars die
No the web isn’t dead. And it certainly won’t be killed by “apps.” Apps — particularly those that are primarily for searching and consuming information — are almost certainly an anti-pattern. Finding them, installing them, upgrading them, uninstalling them — it’s all a huge pain that users aren’t likely to put up with for much longer unless the app is really compelling. The only thing holding up this process is really access to smartphone’s most powerful features like the camera and filesystem etc.
But I suspect one day the “web” might really end. It won’t be anything dramatic, these things almost never are. It’ll just gradually fade away. Sort of like television. What will kill it won’t be an alternative, competing project but rather something like a substitute good. What the web does best is provide easy access to communication and easy collaboration. Search ties all of this together creating a positive feedback loop. The better the web gets, the better search gets, the better the web gets… But right now this collaboration and communication takes place in silos and often requires massive duplication of data and the hassle of navigating from site to site. What will kill the web will be something that does what the web does but just a bit better. Something that eliminates the problems caused by silos and allows a much more seamless, unified experience. Once this happens, people will find it somewhat strange that individuals used to navigate from site to site to do X, Y and Z. The same way we find it strange that people used to rush home to get home by a certain hour so they could sit in front of a large screen and watch commercials.
So no, the web isn’t dead. But everything dies, even the stars.