Technically yes a lot of processing is done locally. But if you always need access to a service (i.e. a "powerful remote computer") to access your files, and if your device becomes useless without a connection to these services, then it kind of becomes a dumb terminal "philosophically"
But our devices aren't less powerful when offline than they used to be. It's just that networks are better and more ubiquitous, so of course our devices spend more time on networked things like social networking, messaging, browsing memes, etc.
I don't understand this conflation between "we can now almost always be connected to a worldwide computer network" and "now our devices are useless without a network and are now just dumb terminals." To me, the one valid part of this analogy is when applications are artificially reliant on a network connection, like single player games that use the network for DRM, or a web-based image editor whose developers didn't bother supporting offline capabilities. That definitely happens, but it's probably a tiny portion of modern device usage.
In an absolute sense, our devices are more powerful offline than they used to be. But so much of what many people use their devices to do, and so much of the time that spend doing it, are internet-dependent. So in a relative sense, being offline is more crippling in 2017 than it was in 1997.
> That definitely happens, but it's probably a tiny portion of modern device usage.
2/3 of my games are through Steam, and offline play has some complicated restrictions that I've never been bothered to remember. So much software documentation is only available online (especially considering corpora of example code, like StackOverflow). Acquiring new software is often only possible through the Internet. These are things that would've been handled by a visit to the store, or by reading the included documentation. The culture around those things has passed those methods by, for the most part.
I think the only thing the quote gets wrong is the relative balance of power, as the assumption was that remote mainframes would always, due to size constraints, be more powerful than the terminals used to access them.
Of course, the true power imbalance is connectivity, as it has always been. Using the internet is the primary reason most people own computers, and in that sense, our web browser has become our remote terminal. The computing tasks run on most sites doesn't require much more power than you could technically run locally, but the undeniable utility of connecting with other users makes the connection so valuable that the computer is, for most users, entirely useless without the internet.
I have sometimes wondered that what made the "web" special compared to the earlier BBS and leased terminal attempts is that we can have multiple "connections" up at the same time.
If the C64 back then could have brought up 5+ BBSs/terminals at once for various services, we could basically be looking at the same as a browser with 5+ tabs open to various sites/services.
For some reason lot of people seem to find it hard to imagine that there could be a mid-way system between the extremes of client/server - and that in fact the hybrid system is what we have today, where there's a genuine mix of local processing and storage for some tasks, with remote processing and storage for others.
More, that the app economy is very much this hybrid, where users buy specific tools to do specific jobs locally, instead of running everything remotely, or independently programming applications from the ground up on their own hardware.
Browsers are almost a side issue, because browsers are like a terminal, but only for a standard selection of popular applications - to some extent the lowest-common-denominator jobs that have the most utility for the widest demographics.
Other jobs and applications still don't fit into the browser, and likely never will - even when there's a benefit to being able to collaborate. (E.g. I can't make music in my browser. If I want to collaborate I still have to send files over the Internet and wait for someone to edit them. Or I can use a mediocre collaboration system built into a DAW. But technically and socially, there are too many limitations to the in-browser experience to expect that live collaboration will become a thing soon.)