The diversity of interests that people have is being completely ignored when predictions of the end of websites are made.
Professional webmasters (i.e. who do, or hope to, get paid for our efforts) can easily forget that many people have deep interest in a topic and run their site as a hobby rather than a business; and running a website isn't expensive (if your time is given freely and as long as you don't get inundated with traffic). We should also remember that any niche that does not attract much advertising spend is unlikely to be forced out of existence by corporations - even Demand Media has a point where they say no.
I absolutely agree that some, mainly popular, elements of the web/net have changed or will do soon so that small players are marginalised or eliminated but extrapolating that to predict the end of the web is just plain wrong.
Why niche will remain; an offline/online comparison.
Let's take the example of offline businesses, it's certainly true that many mega-corporations exist now (something that was not the case before) and they control certain sectors (just look at food where you have only a few huge supermarket groups dealing with only a few huge food groups and "owning" the market). Mega-corporations are to offline as Google or Facebook are to online, but there are still many medium and small businesses that are in the food business; mainly because of convenience (which we can exclude on the web as distances are not physical) or because they are specialised (the niche player on the web). The nature of supermarkets is such that they can never cater for every niche food, doing that ruins their business model; so specialists can be small and that can be a defence in some ways. There are verticals that there will be no room for specialists, but many verticals NEED specialists to cater for the diverse requirements of the marketplace. Niche players will have more loyal customers/users who value the service or information more than the technological delivery method - I've seen many tremendously useful hobbyist sites where I know that person struggles to build a site so expecting them to migrate to another platform (or many such platforms) is not going to happen. Faced with the choice of using an "old" technology such as a website to get to information that is not available elsewhere is an easy one to know the response to, people will use the website in the same way that books are still used today.
Some things are not meant for corporates!
Another example from the offline world (that resonates particularly well with the hobbyist site) is the role that charities play. Can you imagine a corporate moving into every sector that charities cater for? I certainly can't. Some things are not interesting to corporations (OK, they might support charities but that's often their CSR departments "doing good" or "giving back").
The service provided by charities is more important than them being located in a swanky office or a shiny new shop - in the same way, online, people will seek them out and will not mind if they don't have an app or if they are not on Facebook - this means that websites will remain a great source of information for people who have a specific need and who trust the source (in fact, a website will probably be mandatory for many such organisations so as not to discriminate against people seeking the service - as it's widely available and tools exist for it that cater for disabilities).
Can you extrapolate a decline in web usage to the end of the web?
Not with any level of confidence! Lets look at why the percentage of usage has changed;
People are lazy and cheap! (a person may not be but people in general are) The availability of streamed movies probably takes some users away from offline stores, but it also attracts users that simply would not have used that time for watching a movie. The greater availability of services in a simple and immediate form will create massive, and probably unpredictable, changes to the way the public spends it's time (even though many of the same options were available before, some barrier such as cost, time or opportunity cost has been removed). Whatever happens with usage in those big areas such as entertainment is significant but it does not cater for informational requirements.
Also, It's likely that aimless browsing has been lessened as options increase to allow for long interactions to occur (movie watching, game playing, social...). People will choose to spend their free time in changing ways, but there will always be actions that are not deemed to be free time exercises (such as researching work stuff or finding a contractor to fix a problem).
So what will remain a web activity and why? (and why app to web will remain)
We must remember that people can learn to go to a particular site (even if that means searching for that brand) if they do it often enough and if it gives them a reason to come back - this is a simple idea to do with brand building; so the activities that people like/need to do often are likely to promote the ability for brands to be built (and apps to be successful). But what about the type of need that is so infrequent that someone will not remember brands (let's say finding a plumber or searching for an unusual piece of information). Of course we must also remember that some people will use a service often enough for brands to be important whereas others will see the service as a one use affair (e.g. a regular hill-walker needing a new tent versus a music festival camper in need of a tent - both use an outdoor goods shop but one will know much about that vertical and the other will see it as a one-off purchase and hence forget who they bought the tent from). The lesson here is that even well established "verticals" can be treated as niche by some users.
So, given that many people will see verticals as a niche they need a way to access that information in a way that differs from say an app that they have chosen to be a permanent feature on their phone (as an example, how many people reading this have an app on their phone right now that is for something they have not needed in the last year?). The occasional need is where a service such as Google pops up as the choice most people will make; that may be through an app to do the search but it's likely that the user will end up on a website (even if they then go on to install an app for that provider for some reason).
Another reason that the web will remain for a very long time is the need for the likes of Google to offer a complete search - people will lose faith with Google if they exclude even a small percentage of the things they search for. As long as Google has a competitor, and probably even if they do not, they will feel the need to continue offering web results; they may favour other delivery methods in the future but if an app does not exist that answers the query, what other option is there?