@ maflynn,
The majority of that site you linked is handling all of its effects and so on via JavaScript and SVG(Maybe canvas, I didn't look.) -- or as the kids call it... HTML5 (Since it's become a blanket term these days). It's AJAX. There's only a few areas they use Flash on that site. You can left-click(control-click) to see if an element is Flash.
Flash like AJAX has had access to back, forward, address bar, and refresh button for years now, but the developer has to know how to implement support for it. It's called deep-linking. It takes a bit more effort and understanding though than some care to commit, but for a product site it should be a given -- since a direct link to a product that can be copied and pasted is always useful.
@ elppa,
So says the individual with an iOS avatar.
@ bedifferent,
Flash is not being abandoned, don't believe the haters -- well that .01% of Apple product using Job ... er ... supporters. A substantial majority, so pretty much everybody else is still behind Flash since HTML5 does not do what FLash can do.
Your question is either or, but you really need both, especially if you want to stay competitive.
Flash on its own can not access the browser DOM and even if you build an stand alone app, CSS is quite useful for formatting text, just as it is in HTML -- but you'l also have access to more advanced text-formatting that goes beyond anything that can be done with HTML/JS and CSS right now.
HTML5 on the other hand still falls noticeably short of what FLash is capable of doing and there's that tid-bit that it's not even a standard. Even it it were, it still has the same cross-browser/platform limitations as HTML4 AJAX. Nothing has really changed... BUT, having siad that, there are many aspects of HTML5 development that you'll want, well need to learn even when developing Flash content.
Just for reference: I've been doing web and interactive development since 95 and In order to build something in Flash now days, I use any of the fallowing in any combination; ActionScript 3(Flash's programming language, it has a descent IDE to work in.), JavaScript, ASP or PHP, XML or JSON, MySQL or SQL, and of course HTML and CSS, along with the experience to know how to optimize both my art assets, but also my code -- I've always hated bloat no matter what tool is being used!
Anyways, there's WAY more to this, but don't limit yourself with just HTML5 or Flash for that matter. You really need to learn both if you want to be busy busy busy!