Let's have a look at the past, and see if we can understand the present and, within limits, forecast the future. This is, I believe, the only way to understand Andreessen.
Language -- creation and break-up
Apps today are distributed through many incompatible application stores. This reminds me the tower of Babel: great enthusiasm with the invention of language, but then people start talking different languages. If you look at any information revolution, not just the creation of language, the pattern has always been the same. Humanity creates a tool for exchanging information, and then breaks this tool into many tools, similar but yet incompatible between each other. It it neither good nor bad –it is just inevitable, and for good reasons (you need the language to be more specific in-between your community) which we shouldn't analyze here. The question is: does it sound familiar? Well, yes!
How Apple saved the publishers
Apple, and all the other corporations who followed it, gave new life to the web. Five years ago, newspapers, movies and music publishers were lamenting: "How will we survive if no one wants to pay for reading an article?".
A few years later, with the introduction of the App Store, every one got happy. Users can access information from their mobile, and publishers can easily charge for it. Soon, similar, but incompatible application stores appeared. Apple, rightfully, wants to defend its dominant position, and refuses to have others' application stores on the iPhone. Apple would like (it seems) to sell an iPhone to every single human being, so we can all buy on the App Store. This might be a bit too much, even for Apple.
Why applications have to change
If I were an enterpreneur or a developer, I didn't want Apple to impose on me its technology, even if it is a good technology. This is why I am waiting for html5 to be good enough to be used for serious stuff. Once I have my app developed in html5, I can sell it on any possible app-store --be Google Play, Amazon Store or "the" App Store. Maybe, the free version of my app will be available on the web.
In addition to that, as a user I don't want Apple to decide which app I can have and which I cannot. Government's sensorship is more than enough. This is more important than it may seem to Apple: without free exchange of information, humanity will go backward, not forward.
Apple and Manuzio, evolution of the revolution
And we will go forward. We are living in the middle of the biggest information revolution after the mobile types one. When modern press was invented. The revolution we are living will still deliver high quality, free information to humanity, exactly like books and newspapers did from Guthenberg on. If Netscape was Guthenberg, Apple is the new Aldus Manuzio, the Renaissance publisher who set up a definite scheme of book design, and introduced small and pocket editions (mobile editions...) of books. Manuzio became rich, but many followed his step, like many have followed Apple's step.
This revolution will also be remunerative! Following the Apple business model, some young publishers are already able to leverage on new tools for information exchange (books, movies, magazines, music etc). As publishers have to change their vision, many old publishers, AKA the dinosaurs, will die.
Last, we need someone pointing us to the right app/websites when looking for it, exactly like Google did 15 years ago. At the moment, apps are more like monads which hardly interact between each other. And in the absence of a network, it's hard to understand who's the leader... but we are already seeing huge efforts in this direction, and this will soon happen.
In conclusion, I think we can interpret Andressen like saying: "The web is alive, and is doing pretty well. Apps are good, but they are closed. This means they will soon change, and we will have application-like websites, able to pay salaries to journalists and musicians, but also accessible by everyone with a pocket size
computers, like Manuzio would call smart-phones.
PS The Tower of Bable, from Genesis:
And the whole earth [Internet] was of one language [http]. And they [the users] said: "Go to, let us build us a city and a tower, whose top may reach unto heaven; and ... lest we be scattered abroad upon the face of the whole earth. [Lest we call this the "World Wide Web"]
And the Lord [Corporations] said: "Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do." [or: we thought the web was a huge supermarket, but people started using it for exchanging movies and read news and books for free. How will we survive? And honestly, shouldn't people pay when using the product of the work of some one else?]
"Go to, let us go down, and there confound their language, that they may not understand one another's speech."
[And the application stores were created.]