It works in Internet Explorer, Edge, and the CDF Player. It certainly hasn't worked in Chrome for a while. I don't know the status for any other browsers.

I'm not happy about the more limited options either but does it not work with the CDF Reader? (which is required to be installed in any event)

Many of the demos have animations showing some of the functionality (using Adobe Flash Player which I thought by decree would never be allowed on a Mac) but if one needed to run a CDF, then one needed to download the CDF Player. It's always been that way (as far as I know).

Does the browser Plug-In really work with Edge, as indicated by Jim? On a PC with Windows 10, with CDF Player installed, this is the response I get in Edge when selecting one of the featured demonstrations:

Firefox, on the same PC, opens the demo OK.

yes I confirm it doesn't work in safari and firefox

It seems we are now in a situation where Firefox, Safari and probably Opera also don't work.

The point is that Wolfram have benefited from adopting a publisher/ curator role for these contributions - for example giving guidance as to how they can be quoted as refereed publications. So now - in my opinion- it is up to them to provide and host cloud based versions. I don't think the authors are going to be too happy on a pay per click system when they are basically providing a public domain intellectual contribution. By cloud hosting the demos it seems to me Wolfram would boost the credibility of their new system.

It's certainly the case that browser support for plugins is drying up, and as indicated in my 2015 Wolfram Technology Conference presentation on CDF, our plans for the Demonstration site do indeed involve a switchover to cloud support. This is a process that is in progress right now, but I can't say more about the timetable. There will be no shortage of announcements as we roll out our updated site, so please stay tuned!

I don't find any problem using Safari on Mac OS X. From the Website http://demonstrations.wolfram.com, just find the Demonstration you want and click on it. If the free Wolfram CDF player is installed, the Demo is then fully functional.

It would be nice if the user had an option on the Website to automatically install the CDF player.

I reinstalled the CDF player and indeed, there is no problem any more as Mr. Binder pointed out. I recently upgraded to 10.4 and apparently you also have to upgrade the CDF-player?