Is there any way to trigger the behavior that usually occurs when a mouse is hovered over an element (for example, hovering over your username at the top of a Stack Overflow site) using the Chrome Beta browser?
One way to trigger the hover on links is to long-press the link, wait for the menu to appear, and the press the back button to cancel the menu. This also works in some other browsers.
Note that this doesn't work on all links. Just tried on the example you mentioned, doesn't work, probably because there's a slight delay between the onMouseOver event and showing the menu. But on other pages, where it's a simple onMouseOver trigger this method works.
I don't see how the "hover" effect can be practical on any touchscreen device, regardless of OS.
Screens on most current mobile devices (resistive, capacitive) can only register touch events. You would need to modify the OS to treat a single tap as a mouse pointer, and double-tap as a "click". However other gestures like scrolling, pinch-to-zoom, etc. would most likely stop working with such a paradigm.
Also, most mobile versions of sites disable the fancy stuff like hover animations anyways, in order to load faster.