Many sites use Flash fallbacks. They detect if the browser supports flash, and if it doesn't, they swap in some alternative content instead. Usually it'll be a static image, sometimes it might be a GIF animation or a simple JS widget. Sometimes, if it's a well made fallback, it's almost impossible to tell them apart without using an "inspect element" type DOM inspection tool (which is very difficult to do on mobile devices), especially if the Flash did little beyond offering mouseover interactivity you wouldn't expect on a mobile device anyway.
This isn't a new thing - people did it before Apple stopped supporting Flash, often for users who weren't allowed to install Flash (e.g. government or hospital workers with very locked-down computers). Flash fallbacks are almost as old as Flash itself.
So, on your computers with Flash, you see the Flash version. On mobile devices and computers that don't have Flash, you see whatever they used as a "fallback". It's not flashed, but someone will have worked hard to make it look as much like the Flash widget as possible.
It's not just old or obsolete sites and widgets that use Flash fallbacks.
Occasionally, some modern or semi-modern web widgets prefer flash if it's available, and switch to a modern HTML5 recreation of the Flash features if it isn't. This is often the case when a company has commercially sold some kind of web widget for many years, it was originally in Flash, it's most stable in Flash, so they prefer to use the older, tried-and-tested Flash version if possible because the new HTML5 version is more like a prototype, or because they're worried about varying browser implementations of HTML5.
Very occassionally they have some legitimate non-historical reason for preferring Flash. There are a couple of things Flash does / did that HTML5 doesn't do, which means the Flash version might have features the HTML5 version can't do in a browser. Often these are not pro-user however (e.g. DRM), or niche features involving things like webcams.