First off, there's a small contradiction about offline storage. The author says that users prefer web apps because they take up little-to-no space, but that the web needs to catch up in terms of storage capability. You can't have it both ways - if websites become more offline-heavy, then users will need to get accustomed to managing their available space (as they already do with native apps). This is an as-yet unsolved UX problem for the web.
Also, based on the comments in this thread, I think many people don't realize how far the web has come in terms of offline storage. Today you can build a mobile site that stores MBs of data, launches from the home screen, and works even in airplane mode. (On Android anyway. iOS is another story.)
I built a small site to demonstrate: http://www.pocketjavascript.com/blog/2015/11/23/introducing-.... On an Android phone, Pokedex.org is basically indistinguishable from a native app, at least once you add it to the home screen. In Chrome, tap the green lock and you can see exactly how much space it takes up (around 6MB). Feel free to put your phone in airplane mode and refresh the page - it will still work.
Second off, there's a lot of speculation in the post about Apple's motives, and why they might be throttling back on the web platform relative to Google, Mozilla, and Microsoft. I'm guilty of this myself in "Safari is the new IE," but nowadays I try to have a more nuanced take.
AFAICT, Apple seems to have many small teams with many different motivations, as does Google. Within Google, you'll even find teams that actively undermine other teams - e.g. what the Chrome team is doing with Progressive Web Apps is a direct threat to Android apps. (I'm even surprised to see one team occasionally trash-talking the other on Twitter.) So talking about "Google's motives" or "Apple's motives" as if they're each one big monolithic entity is a little simplistic.
My favorite theory about Apple and the web comes from this article (http://blog.html5test.com/2015/07/safari-and-ie/), which argues that the WebKit team is just too small since the Blink split, which is why they've been having trouble keeping up. No grand conspiracy theory required - just that the team is a little under-financed. Also, Safari is still rocking it in terms of performance and battery life, so it's not like they're asleep at the wheel.
I think the web still has a chance to catch up with native (for a lot of use cases anyway, not all of them), but it will require a change in how we build websites. In the same way that XMLHttpRequest was around for years before web devs "discovered" Ajax, I think offline storage and various mobile APIs might lay dormant for awhile before suddenly everybody is taking advantage of them. As web developers, the ball is in our court.